Research Papers

List of scientific papers in the reverse chronological order:

2026

1. A. Choudhry, Three integers whose sum, product, and the sum of the products of the integers, taken two at a time, are perfect squares, Integers 26 (2026), Paper No. A35, 15 pp. DOI: 10.5281/zenodo.18714492.

2. A. Choudhry, Expressing three consecutive integers as sums of three cubes, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 30 (2026), no. 570, 51–63. DOI: 10.21857/ygjwrce5ry.

3. A. Choudhry, Two sets of integers such that all elements of the sumset of the two sets are perfect squares, Integers 26 (2026), Paper No. A66, 17 pp. DOI: 10.5281/zenodo.20597480.

4. A. Choudhry, Circles with four rational points in geometric progression, Rocky Mountain J. Math. 56 (2026), no. 2, 367–379. DOI: 10.1216/rmj.2026.56.367.

2025

1. A. Choudhry, Arithmetic progressions represented by binary quadratic forms, Integers 25 (2025), Paper No. A14, 9 pp. DOI: 10.5281/zenodo.14907299.

2. A. Choudhry and A. S. Zargar, The Diophantine equation x⁴+y⁴=z⁴+w⁴, Funct. Approx. Comment. Math. 72 (2025), no. 1, 95–102. DOI: 10.7169/facm/240530-10-7.

2024

1. A. Choudhry and B. Maji, Finite sequences of integers expressible as sums of two squares, Int. J. Number Theory 20 (2024), no. 7, 1755–1766. DOI: 10.1142/s1793042124500866.

2. A. Choudhry, Expressing an integer as a sum of cubes of polynomials, Integers 24 (2024), Paper No. A26, 7 pp. DOI: 10.5281/zenodo.10821687.

3. A. Choudhry, Rational quadrilaterals, Rocky Mountain J. Math. 54 (2024), no. 1, 83–96. DOI: 10.1216/rmj.2024.54.83.

2023

1. A. Choudhry, Two pairs of biquadrates with equal sums, Integers 23 (2023), Paper No. A53, 4 pp. DOI: 10.5281/zenodo.8214806.

2. A. Choudhry and A. S. Zargar, An octic Diophantine equation and related families of elliptic curves, Int. J. Number Theory 19 (2023), no. 8, 1967–1976. DOI: 10.1142/s179304212350094x.

2022

1. A. Choudhry, Ideal solutions of the Tarry–Escott problem of degree seven, Integers 22 (2022), Paper No. A115, 10 pp. DOI: 10.5281/zenodo.10999357.

2. A. Choudhry, Matrix morphology and composition of higher degree forms with applications to Diophantine equations, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 26 (2022), no. 551, 65–89. DOI: 10.21857/moxpjh1n5m.

3. A. Choudhry and A. S. Zargar, Pairs of equiperimeter and equiareal triangles whose sides are perfect squares, Funct. Approx. Comment. Math. 66 (2022), no. 2, 245–251. DOI: 10.7169/facm/1985.

4. A. Choudhry, I. Bluskov, and A. James, A Diophantine equation inspired by Brahmagupta's identity, Int. J. Number Theory 18 (2022), no. 4, 905–911. DOI: 10.1142/S1793042122500476.

5. A. Choudhry and O. Couto, A new Diophantine equation involving fifth powers, Acta Arith. 202 (2022), no. 1, 43–53. DOI: 10.4064/aa210419-4-7.

2021

1. A. Choudhry, A Diophantine problem concerning third order matrices, Serdica Math. J. 47 (2021), no. 2, 153–160. DOI: 10.55630/serdica.2021.47.153-160.

2. A. Choudhry, Some Diophantine problems concerning a pair of rational triangles with a common circumradius, Integers 21 (2021), Paper No. A110, 12 pp. DOI: 10.5281/zenodo.10839470.

3. A. Choudhry, New solutions of the Tarry–Escott problem of degrees 2, 3 and 5, J. Integer Seq. 24 (2021), no. 8, Article 21.8.1, 9 pp.

4. A. Choudhry and A. S. Zargar, A sextic Diophantine chain and a related Mordell curve, Integers 21 (2021), Paper No. A39, 12 pp. DOI: 10.5281/zenodo.10816767.

5. A. Choudhry, Four biquadrates whose sum is a perfect square, J. Integer Seq. 24 (2021), no. 1, Article 21.1.8, 7 pp.

2020

1. A. Choudhry, Cyclic pentagons and hexagons with integer sides, diagonals and areas, Serdica Math. J. 46 (2020), no. 4, 307–322.

2. A. Bremner and A. Choudhry, The Fermat cubic and quartic curves over cyclic fields, Period. Math. Hungar. 80 (2020), no. 2, 147–157. DOI: 10.1007/s10998-019-00297-y.

3. A. Choudhry, An improvement of Prouhet's 1851 result on multigrade chains, Int. J. Number Theory 16 (2020), no. 7, 1425–1432. DOI: 10.1142/s179304212050075x.

4. A. Choudhry, A Diophantine system, Integers 20 (2020), Paper No. A27, 6 pp. DOI: 10.5281/zenodo.10776476.

5. A. Choudhry, Brahmagupta quadrilaterals with equal perimeters and equal areas, Int. J. Number Theory 16 (2020), no. 3, 523–535. DOI: 10.1142/s1793042120500268.

6. A. Choudhry and A. S. Zargar, A parametrised family of Mordell curves with a rational point of order 3, Notes Number Theory Discrete Math. 26 (2020), no. 1, 40–44. DOI: 10.7546/nntdm.2020.26.1.40-44.

2019

1. A. Choudhry, The algebraic solution of unilateral matrix polynomial equations, Serdica Math. J. 45 (2019), no. 4, 325–340.

2. A. Choudhry, Symmetric Diophantine systems and families of elliptic curves of high rank, Rocky Mountain J. Math. 49 (2019), no. 5, 1419–1447. DOI: 10.1216/rmj-2019-49-5-1419.

2018

1. A. Choudhry and J. Wróblewski, An ancient Diophantine equation with applications to numerical curios and geometric series, Colloq. Math. 151 (2018), no. 1, 1–7 DOI: 10.4064/cm6923-2-2017.

2. A. Choudhry, A Diophantine problem on biquadrates revisited, Math. Stud. 87 (2018), no. 1–2, 129–132. [journal issue PDF]

3. A. Choudhry, A new method of solving certain quartic and higher degree Diophantine equations, Int. J. Number Theory 14 (2018), no. 8, 2129–2154. DOI: 10.1142/s1793042118501282.

4. A. Choudhry, A symmetric Diophantine equation involving biquadrates, Notes Number Theory Discrete Math. 24 (2018), no. 2, 140–144. DOI: 10.7546/nntdm.2018.24.2.140-144.

2017

1. A. Choudhry, A note on the quartic Diophantine equation A⁴+hB⁴=C⁴+hD⁴, Notes Number Theory Discrete Math. 23 (2017), no. 1, 1–3.

2. A. Choudhry and J. Wróblewski, Triads of integers with equal sums of squares and equal products and a related multigrade chain, Acta Arith. 178 (2017), no. 1, 87–100. DOI: 10.4064/aa8574-9-2016.

3. A. Choudhry, A new approach to the Tarry–Escott problem, Int. J. Number Theory 13 (2017), no. 2, 393–417. DOI: 10.1142/s1793042117500233.

2016

1. A. Choudhry, Equal sums of like powers with minimum number of terms, Integers 16 (2016), Paper No. A77, 11 pp. DOI: 10.5281/zenodo.10623321.

2. A. Choudhry and A. Juyal, Rational points in arithmetic progression on the unit circle, J. Integer Seq. 19 (2016), no. 4, Article 16.4.1, 7 pp.

3. A. Choudhry, Quadratic Diophantine equations with applications to quartic equations, Rocky Mountain J. Math. 46 (2016), no. 3, 769–799. DOI: 10.1216/rmj-2016-46-3-769.

4. A. Choudhry, A pair of simultaneous Diophantine equations with no solutions in integers, Math. Stud. 85 (2016), no. 1–2, 163–166.

2015

1. A. Choudhry, An ancient Diophantine problem from the Bijaganita of Bhaskaracharya, Math. Stud. 84 (2015), no. 3–4, 135–139.

2. A. Choudhry, Some Diophantine equations concerning biquadrates, Notes Number Theory Discrete Math. 21 (2015), no. 4, 1–5.

3. A. Choudhry, Arithmetic progressions on Huff curves, J. Integer Seq. 18 (2015), no. 5, Article 15.5.2, 9 pp.

4. A. Choudhry, A Diophantine problem from calculus, J. Number Theory 153 (2015), 354–363. DOI: 10.1016/j.jnt.2015.01.010.

5. A. Choudhry, Sextuples of integers whose sums in pairs are squares, Int. J. Number Theory 11 (2015), no. 2, 543–555. DOI: 10.1142/s1793042115500281.

2014

1. A. Choudhry, Arithmetic progressions of rectangles on a conic, Notes Number Theory Discrete Math. 20 (2014), no. 4, 53–57.

2. A. Bremner, A. Choudhry, and M. Ulas, Constructions of diagonal quartic and sextic surfaces with infinitely many rational points, Int. J. Number Theory 10 (2014), no. 7, 1675–1698. DOI: 10.1142/S179304211450050X.

3. A. Choudhry and J. Wróblewski, Three triads of integers with equal sums of squares and cubes, Rocky Mountain J. Math. 44 (2014), no. 2, 435–441. DOI: 10.1216/rmj-2014-44-2-435.

2013

1. A. Choudhry, Quintuples of positive integers whose sums in pairs or in triples are squares, Enseign. Math. (2) 59 (2013), no. 3–4, 337–349. DOI: 10.4171/lem/59-3-7.

2. A. Choudhry and J. Wróblewski, A quintic Diophantine equation with applications to two Diophantine systems concerning fifth powers, Rocky Mountain J. Math. 43 (2013), no. 6, 1893–1899. DOI: 10.1216/rmj-2013-43-6-1893.

3. A. Choudhry, Equal sums of like powers and equal products of integers, Rocky Mountain J. Math. 43 (2013), no. 3, 763–792. DOI: 10.1216/rmj-2013-43-3-763.

2012

1. A. Choudhry, Triads of integers with equal sums and equal products, Math. Stud. 81 (2012), no. 1–4, 185–188.

2. A. Choudhry and J. Wróblewski, A symmetric Diophantine system concerning fifth powers, Acta Arith. 155 (2012), no. 1, 91–95. DOI: 10.4064/aa155-1-9.

2011

1. A. Choudhry, Quadratic form made a perfect power by a new composition theorem on arbitrary quadratic forms, Enseign. Math. (2) 57 (2011), no. 1–2, 91–102. DOI: 10.4171/lem/57-1-4.

2. A. Choudhry, Equal sums of like powers, both positive and negative, Rocky Mountain J. Math. 41 (2011), no. 3, 737–763. DOI: 10.1216/rmj-2011-41-3-737.

2010

1. A. Choudhry, Some Diophantine problems concerning equal sums of integers and their cubes, Hardy-Ramanujan J. 33 (2010), 59–70. DOI: 10.46298/hrj.2010.171.

2009

1. A. Choudhry, Some exponential Diophantine equations, Math. Stud. 78 (2009), no. 1–4, 227–232. [journal issue PDF]

2. A. Choudhry, A Diophantine equation of Mordell, J. Ramanujan Math. Soc. 24 (2009), no. 2, 113–126. [journal issue]

2008

1. A. Choudhry and J. Wróblewski, Ideal solutions of the Tarry–Escott problem of degree eleven with applications to sums of thirteenth powers, Hardy-Ramanujan J. 31 (2008), 1–13. DOI: 10.46298/hrj.2008.161.

2007

1. A. Choudhry, On squares of squares, Math. Stud. 76 (2007), no. 1–4, 247–255. [journal issue PDF]

2. A. Choudhry, Several arithmetic progressions of equal lengths and equal products of terms, Enseign. Math. (2) 53 (2007), no. 1–2, 87–95.

3. A. Choudhry and J. Wróblewski, Quartic Diophantine chains, Acta Arith. 128 (2007), no. 4, 339–348. DOI: 10.4064/aa128-4-3.

4. A. Choudhry, Rational triangles with the same perimeter and the same area, Hardy-Ramanujan J. 30 (2007), 19–30. DOI: 10.46298/hrj.2007.158.

2006

1. A. Choudhry, Matrix analogues of the Tarry–Escott problem, multigrade chains and the equation of Fermat, Math. Stud. 75 (2006), no. 1–4, 215–224. [journal archive; individual article link not located]

2. A. Choudhry, The algebraic structure of the set of integer solutions of a quadratic Diophantine equation, Math. Stud. 75 (2006), no. 1–4, 197–201. [journal archive; individual article link not located]

3. A. Choudhry, A Diophantine system, Math. Stud. 75 (2006), no. 1–4, 239–241. [journal archive; individual article link not located]

4. A. Choudhry, Integer solutions of linear Diophantine equations form a group, Missouri J. Math. Sci. 18 (2006), no. 2, 135–141. DOI: 10.35834/2006/1802135.

5. A. Choudhry, Points at rational distances on a parabola, Rocky Mountain J. Math. 36 (2006), no. 2, 413–424. DOI: 10.1216/rmjm/1181069460.

6. K. K. Nwabueze and A. Choudhry, Some normal extensions of the Diophantine group, Int. Math. Forum 1 (2006), no. 25–28, 1249–1253. DOI: 10.12988/imf.2006.06103.

2005

1. A. Choudhry, Parametric solutions of the quartic Diophantine equation f(x,y) = f(u,v), Rocky Mountain J. Math. 35 (2005), no. 5, 1467–1477. DOI: 10.1216/rmjm/1181069646.

2. A. Choudhry, Symmetric Diophantine systems revisited, Acta Arith. 119 (2005), no. 4, 329–347. DOI: 10.4064/aa119-4-3.

3. K. K. Nwabueze, O. Kihel, and A. Choudhry, Defining a group operation on the set of solutions of the parametrised quadratic Diophantine equation, Int. J. Pure Appl. Math. 18 (2005), no. 4, 441–444.

4. A. Choudhry, A Diophantine problem concerning cubes, J. Number Theory 110 (2005), no. 2, 403–412. DOI: 10.1016/j.jnt.2004.07.013.

5. A. Choudhry, The complete solution of a Diophantine equation involving biquadrates, J. Number Theory 110 (2005), no. 2, 317–324. DOI: 10.1016/j.jnt.2004.07.012.

6. A. Choudhry, Some Diophantine equations involving sixth powers, Math. Stud. 74 (2005), no. 1–4, 231–236. [journal archive; individual article link not located]

2004

1. A. Choudhry, A Diophantine system related to the Tarry–Escott problem with no non-trivial solutions, Indian J. Pure Appl. Math. 35 (2004), no. 12, 1395–1398. [journal archive; individual article link not located]

2. A. Choudhry and K. K. Nwabueze, An example of a group, Int. J. Pure Appl. Math. 15 (2004), no. 3, 397–400. [journal archive; individual article link not located]

3. A. Choudhry, Symmetric Diophantine equations, Rocky Mountain J. Math. 34 (2004), no. 4, 1281–1298. DOI: 10.1216/rmjm/1181069800.

4. A. Choudhry, Extraction of n-th roots of 2×2 matrices, Linear Algebra Appl. 387 (2004), 183–192. DOI: 10.1016/j.laa.2004.02.010.

2003

1. A. Choudhry, Ideal solutions of the Tarry–Escott problem of degrees four and five and related Diophantine systems, Enseign. Math. (2) 49 (2003), no. 1–2, 101–108. DOI: 10.5169/seals-66681.

2. A. Choudhry, Triads of integers with equal sums of squares, cubes and fourth powers, Bull. Lond. Math. Soc. 35 (2003), no. 6, 821–824. DOI: 10.1112/s0024609303002388.

2002

1. A. Choudhry, On the solvability of two simultaneous symmetric cubic Diophantine equations with applications to sextic Diophantine equations, Rocky Mountain J. Math. 32 (2002), no. 1, 91–104. DOI: 10.1216/rmjm/1030539609.

2001

1. A. Choudhry, A cubic Diophantine equation and a related Diophantine chain, Indian J. Pure Appl. Math. 32 (2001), no. 9, 1421–1428. [journal archive; individual article link not located]

2. A. Choudhry, Equal sums of like powers, Rocky Mountain J. Math. 31 (2001), no. 1, 115–129. DOI: 10.1216/rmjm/1008959671.

3. A. Choudhry, On the solvability of quintic and sextic Diophantine equations of the type f(x,y) = f(u,v), J. Number Theory 88 (2001), no. 2, 225–240. DOI: 10.1006/jnth.2000.2603.

4. A. Choudhry, The system of simultaneous equations Σ₁³xᵢᵏ = Σ₁³yᵢᵏ, k = 1, 2, 5, has no non-trivial solutions in integers, Math. Stud. 70 (2001), no. 1–4, 85–88. [journal archive; individual article link not located]

5. A. Choudhry, Triads of cubes with equal sums and equal products, Math. Stud. 70 (2001), no. 1–4, 137–143. [journal archive; individual article link not located]

6. A. Choudhry, Triads of biquadrates with equal sums and equal products, Math. Stud. 70 (2001), no. 1–4, 149–152. [journal archive; individual article link not located]

7. A. Choudhry, On a quartic Diophantine equation, Math. Stud. 70 (2001), no. 1–4, 181–183. [journal archive; individual article link not located]

8. A. Choudhry, On representing 1 as the sum or difference of kth powers of integers, Math. Stud. 70 (2001), no. 1–4, 205–208. [journal archive; individual article link not located]

9. A. Choudhry, On the number of representations of an integer as a sum of four integral fifth powers, Math. Stud. 70 (2001), no. 1–4, 215–217. [journal archive; individual article link not located]

2000

1. A. Choudhry, Ideal solutions of the Tarry–Escott problem of degree four and a related Diophantine system, Enseign. Math. (2) 46 (2000), no. 3–4, 313–323. DOI: 10.5169/seals-64802.

2. A. Choudhry, Equal sums of seventh powers, Rocky Mountain J. Math. 30 (2000), no. 3, 849–852. DOI: 10.1216/rmjm/1021477247.

3. A. Choudhry, On equal sums of sixth powers, Rocky Mountain J. Math. 30 (2000), no. 3, 843–848. DOI: 10.1216/rmjm/1021477246.

4. A. Choudhry, Equal sums of powers of the terms of arithmetic progressions of equal lengths, Rocky Mountain J. Math. 30 (2000), no. 1, 149–156. DOI: 10.1216/rmjm/1022008981.

5. A. Choudhry, On sums of seventh powers, J. Number Theory 81 (2000), no. 2, 266–269. DOI: 10.1006/jnth.1999.2465.

1999

1. A. Choudhry, An elementary method of solving certain Diophantine equations, Math. Stud. 68 (1999), no. 1–4, 195–199. [journal archive; individual article link not located]

2. A. Choudhry, The general solution of a cubic Diophantine equation, Ganita 50 (1999), no. 1, 1–4. [journal archive; individual article link not located]

3. A. Choudhry, The Diophantine equation ax⁵+by⁵+cz⁵=au⁵+bv⁵+cw⁵, Rocky Mountain J. Math. 29 (1999), no. 2, 459–462. DOI: 10.1216/rmjm/1181071645.

4. A. Choudhry, On the quartic Diophantine equation f(x,y) = f(u,v), J. Number Theory 75 (1999), no. 1, 34–40. DOI: 10.1006/jnth.1998.2322.

1998

1. A. Choudhry, A Diophantine equation involving fifth powers, Enseign. Math. (2) 44 (1998), no. 1–2, 53–55. DOI: 10.5169/seals-63895.

2. A. Choudhry, On triads of squares with equal sums and equal products, Ganita 49 (1998), no. 2, 101–106. [journal archive; individual article link not located]

3. A. Choudhry, On equal sums of cubes, Rocky Mountain J. Math. 28 (1998), no. 4, 1251–1257. DOI: 10.1216/rmjm/1181071714.

4. A. Choudhry, The Diophantine equation A⁴+4B⁴=C⁴+4D⁴, Indian J. Pure Appl. Math. 29 (1998), no. 11, 1127–1128. [journal archive; individual article link not located]

1997

1. A. Choudhry, The Diophantine equation X₁⁵+X₂⁵+2X₃⁵=Y₁⁵+Y₂⁵+2Y₃⁵, Ganita 48 (1997), no. 2, 115–116. [journal archive; individual article link not located]

2. A. Choudhry, On equal sums of fifth powers, Indian J. Pure Appl. Math. 28 (1997), no. 11, 1443–1450. [journal archive; individual article link not located]

3. A. Choudhry, On arithmetic progressions of equal lengths and equal products of terms, Acta Arith. 82 (1997), no. 1, 95–97. DOI: 10.4064/aa-82-1-95-97.

1995

1. A. Choudhry, On the Diophantine equation A⁴+hB⁴=C⁴+hD⁴, Indian J. Pure Appl. Math. 26 (1995), no. 11, 1057–1061. [journal archive; individual article link not located]

1994

1. A. Choudhry, On equal sums of sixth powers, Indian J. Pure Appl. Math. 25 (1994), no. 8, 837–841. [journal archive; individual article link not located]

1992

1. A. Choudhry, Multigrade chains with odd exponents, J. Number Theory 42 (1992), no. 2, 134–140. DOI: 10.1016/0022-314x(92)90017-j.

2. A. Choudhry and A. Schinzel, On the number of terms in the irreducible factors of a polynomial over ℚ, Glasg. Math. J. 34 (1992), no. 1, 11–15. DOI: 10.1017/S001708950000848X.

1991

1. A. Choudhry, The Diophantine equation A⁴+B⁴=C⁴+D⁴, Indian J. Pure Appl. Math. 22 (1991), no. 1, 9–11. [journal archive; individual article link not located]

2. A. Choudhry, The Diophantine system Σ₁⁴xᵢʳ = Σ₁⁴yᵢʳ, r = 1, 3, 5, Bull. Calcutta Math. Soc. 83 (1991), no. 1, 85–86. [journal archive; individual article link not located]

3. A. Choudhry, Symmetric Diophantine systems, Acta Arith. 59 (1991), no. 3, 291–307. DOI: 10.4064/aa-59-3-291-307.

4. A. Choudhry, On sums of eighth powers, J. Number Theory 39 (1991), no. 1, 104–107. DOI: 10.1016/0022-314x(91)90037-c.

1989

1. A. Choudhry, Representation of every rational number as an algebraic sum of fifth powers of rational numbers, Enseign. Math. (2) 35 (1989), no. 1–2, 19–20. DOI: 10.5169/seals-57359.

1988

1. A. Choudhry, On Fermat's Last Theorem, Elem. Math. 43 (1988), no. 6, 182–183.

Accepted for publication

1. A. Choudhry, An arbitrary number of squares whose sum, on excluding any one of them, is also a square, preprint, arXiv:2505.01667 [math.NT] (2025); accepted for publication, Rocky Mountain J. Math. [accepted; preprint]