Publications


  1. On Fermat's last theorem, Elemente der Mathematik 43 (1988), 182--183.

  2. Representation of every rational number as an algebraic sum of fifth powers of rational numbers, L'Enseignement Mathematique 35 (1989), 19--20.

  3. On sums of eighth powers, Journal of Number Theory 39 (1991), 104--107.

  4. The diophantine equation $A^{4}+B^{4}=C^{4}+D^{4},$ Indian Journal of Pure and Applied Mathematics 22 (1991), 9--11.

  5. The diophantine system $\sum_{1}^{4} x_{i}^{r}=\sum_{1}^{4} y_{i}^{r},\;r=1,3,5,$ Bulletin of the Calcutta Mathematical Society, 83 (1991), 85--86.

  6. Symmetric diophantine systems, Acta Arithmetica 59 (1991), 291--307.

  7. Multigrade chains with odd exponents, Journal of Number Theory 42 (1992), 134--140.

  8. (written jointly with A. Schinzel) On the number of terms in the irreducible factors of a polynomial over Q, Glasgow Mathematical Journal 34 (1992), 11--15.

  9. On equal sums of sixth powers, Indian Journal of Pure and Applied Mathematics 25 (1994), 837--841.

  10. On the diophantine equation $A^{4}+hB^{4}=C^{4}+hD^{4}$, Indian Journal of Pure and Applied Mathematics 26 (1995), 1057--1061.

  11. On equal sums of fifth powers, Indian Journal of Pure and Applied Mathematics 28 (1997), 1443--1450.

  12. The diophantine equation $X_{1}^{5}+X_{2}^{5}+2X_{3}^{5} =Y_{1}^{5}+Y_{2}^{5}+2Y_{3}^{5},$ Ganita 48 (1997), 115--116.

  13. On arithmetic progressions of equal lengths and equal products of terms, Acta Arithmetica 82 (1997), 95--97.

  14. On equal sums of cubes, Rocky Mountain Journal of Mathematics 28 (1998), 1251--1257.

  15. The diophantine equation $A^{4}+4B^{4}=C^{4}+4D^{4}$, Indian Journal of Pure Applied Mathematics 29 (1998), 1127--1128.

  16. On triads of squares with equal sums and equal products, Ganita 49 (1998), 101--106.

  17. A diophantine equation involving fifth powers, L'Enseignement Mathematique 44 (1998), 53--55.

  18. The diophantine equation $ax^{5}+by^{5}+cz^{5}=au^{5}+bv^{5}+cw^{5}$, Rocky Mountain Journal of Mathematics 29 (1999), 459--462.

  19. An elementary method of solving certain diophantine equations,The Mathematics Student 68 (1999), 195--199.

  20. On the quartic diophantine equation $f(x,y)=f(u,v),$ Journal of Number Theory 75 (1999), 34--40.

  21. The general solution of a cubic diophantine equation, Ganita 50 (1999), 1--4.

  22. Equal sums of powers of the terms of arithmetic progressions of equal lengths, Rocky Mountain Journal of Mathematics 30 (2000), 149--156.

  23. On equal sums of sixth powers, Rocky Mountain Journal of Mathematics 30 (2000), 843--848.

  24. Equal sums of seventh powers, Rocky Mountain Journal of Mathematics 30 (2000), 849--852.

  25. On sums of seventh powers, Journal of Number Theory 81 (2000), 266--269.

  26. Ideal solutions of the Tarry-Escott problem of degree four and a related diophantine system, L'Enseignement Mathematique 46 (2000), 313--323.

  27. Equal sums of like powers, Rocky Mountain Journal of Mathematics 31 (2001), 115--129.

  28. On the number of representations of an integer as a sum of four integral fifth powers, The Mathematics Student 70 (2001), 215--217.

  29. On representing 1 as the sum or difference of $k^{th}$ powers of integers, The Mathematics Student 70 (2001), 205--208.

  30. On a quartic diophantine equation, The Mathematics Student 70 (2001), 181--183.

  31. Triads of biquadrates with equal sums and equal products, The Mathematics Student 70 (2001), 149--152.

  32. Triads of cubes with equal sums and equal products, The Mathematics Student 70 (2001), 137--143.

  33. The system of simultaneous equations $\sum_{1}^{3}x_{i}^{k}=\sum_{1}^{3}x_{i}^{k},\;k=1,2$ and 5 has no non-trivial solutions in integers, The Mathematics Student 70 (2001), 85--88.

  34. On the solvability of quintic and sextic diophantine equations of type $f(x,y)=f(u,v)$, Journal of Number Theory 88 (2001), 225--240.

  35. A cubic diophantine equation and a related diophantine chain, Indian Journal of Pure and Applied Mathematics 32 (2001), 1421--1428.

  36. On the solvability of two simultaneous symmetric cubic diophantine equations with applications to sextic diophantine equations, Rocky Mountain Journal of Mathematics 32 (2002), 91--104.

  37. Ideal solutions of the Tarry-Escott problem of degrees four and five and related diophantine systems, L'Enseignement Mathematique 49 (2003), 101--108.

  38. Triads of integers with equal sums of squares, cubes and fourth powers, Bulletin of the London Mathematical Society 35 (2003), 821--824.

  39. Symmetric diophantine equations, Rocky Mountain Journal of Mathematics 34 (2004), 1279--1296.

  40. Extraction of $n$th roots of $2 \times 2$ matrices, Linear Algebra and its Applications 387 (2004), 183--192.

  41. (written jointly with K. K. Nwabueze) An example of a group, International Journal of Pure and Applied Mathematics 15 (2004), 397--400.

  42. A diophantine system related to the Tarry-Escott problem with no non-trivial solutions, Indian Journal of Pure and Applied Mathematics 35 (2004), 1395--1398.

  43. Parametric solutions of the quartic diophantine equation $f(x,y)=f(u,v)$, Rocky Mountain Journal of Mathematics 35 (2005), 1467--1477.

  44. Some diophantine equations involving sixth powers, The Mathematics Student 74 (2005), 231--236.

  45. A diophantine problem concerning cubes, Journal of Number Theory 110 (2005), 403--412.

  46. The complete solution of a diophantine equation involving biquadrates, Journal of Number Theory 110 (2005), 317--324.

  47. (written jointly with Kenneth Nwabueze and Omar Kihel), Defining a group operation on the set of solutions of the parametrised quadratic Diophantine equation, International Journal of Pure and Applied Mathematics 18 (2005), 441--444 (2005).

  48. Symmetric diophantine systems revisited, Acta Arithmetica 119 (2005), 329--347.

  49. Points at rational distances on a parabola, Rocky Mountain Journal of Mathematics 36 (2006), 413--424.

  50. Integer solutions of linear diophantine equations form a group, Missouri Journal of Mathematics 18 (2006), 135--141.

  51. A diophantine system, The Mathematics Student 75 (2006), 239--241.

  52. Matrix analogues of the Tarry-Escott problem, multigrade chains and the equation of Fermat, The Mathematics Student 75 (2006), 215--224.

  53. The algebraic structure of the set of integer solutions of a quadratic diophantine equation, The Mathematics Student 75 (2006), 197--201.

  54. (written jointly with Kenneth Nwabueze), Some normal extensions of the diophantine group, International Mathematical Forum 1 (2006), 1249--1253.

  55. On squares of squares, The Mathematics Student 76 (2007), 247-255.

  56. Rational triangles with the same perimeter and the same area, Hardy-Ramanujan Journal 30} (2007), 19--30.

  57. Several arithmetic progressions of equal lengths and equal products of terms, L'Enseignement Mathematique 53 (2007), 87--95.

  58. (written jointly with J. Wroblewski) Quartic Diophantine Chains, Acta Arithmetica 128 (2007), 339--348.

  59. (written jointly with J. Wroblewski) Ideal solutions of the Tarry-Escott problem of degree eleven with applications to sums of thirteenth powers, Hardy-Ramanujan Journal 31 (2008), 1--13.

  60. Some exponential diophantine equations, The Mathematics Student 78 (2009), 227-232.

  61. A diophantine equation of Mordell, Journal of Ramanujan Mathematical Society 24 (2009), 113-126.

  62. Some diophantine problems concerning equal sums of integers and their cubes, Hardy-Ramanujan Journal 33 (2010), 59--70.

  63. Equal Sums of Like Powers, both positive and negative, Rocky Mountain Journal of Mathematics 41 (2011), 737--763.

  64. Quadratic form made a perfect power by a new composition theorem on arbitrary quadratic forms, L'Enseignement Mathematique 57 (2011), 91--102.

  65. Triads of integers with equal sums and equal products, The Mathematics Student 81 (2012), 185--188.

  66. (written jointly with J. Wroblewski) A Symmetric Diophantine System Concerning Fifth Powers, Acta Arithmetica 155 (2012), 91--95.

  67. (written jointly with J. Wroblewski) A Quintic Diophantine Equation with applications to Two Diophantine Systems concerning Fifth Powers, Rocky Mountain Journal of Mathematics 43 (2013), 1893--1899.

  68. Equal Sums of Like Powers and Equal Products of Integers, Rocky Mountain Journal of Mathematics 43 (2013), 763--792.

  69. Quintuples of positive integers whose sums in pairs or in triples are squares, L'Enseignement Mathematique 59 (2013), 337--349.

  70. (written jointly with J. Wroblewski) Three Triads of Integers with Equal Sums of Squares and Cubes, Rocky Mountain Journal of Mathematics 44 (2014), 435--441.

  71. (written jointly with A. Bremner and M. Ulas) Constructions of diagonal quartic and sextic surfaces with infinitely many rational points, International Journal of Number Theory 10 (2014), 1675-1698.

  72. Arithmetic progressions of rectangles on a conic, Notes on Number Theory and Discrete Mathematics 20 (2014), 53--57.

  73. Sextuples of integers whose sums in pairs are squares, International Journal of Number Theory 11 (2015), 543--555.

  74. Arithmetic progressions on Huff curves, Journal of Integer Sequences 18 (2015), Paper 15.5.2, 9 pages.

  75. A diophantine problem from calculus, Journal of Number Theory 153 (2015), 354-363.

  76. Some diophantine equations concerning biquadrates, Notes on Number Theory and Discrete Mathematics 21 (2015), 1—5.

  77. An ancient diophantine problem from the Bijaganita of Bhaskaracharya, The Mathematics Student 84 (2015), 135-139.

  78. A pair of simultaneous diophantine equations with no solutions in integers, The Mathematics Student 85 (2016), 163-166.

  79. Quadratic diophantine equations with applications to quartic equations, Rocky Mountain Journal of Mathematics 46 (2016), 769-799.

  80. (written jointly with Abhishek Juyal) Rational Points in Arithmetic Progression on the Unit Circle, Journal of Integer Sequences 19 (2016), Paper 16.4.1, 7 pages.

  81. Equal sums of like powers with minimum number of terms, Integers: Electronic Journal of Combinatorial Number Theory 16 (2016), Paper No. A77, 1-11.

  82. A new approach to the Tarry-Escott problem, International Journal of Number Theory 13 (2017), 393-417.

  83. (written jointly with J. Wroblewski) Triads of Integers with Equal Sums of Squares and Equal Products and a Related Multigrade Chain, Acta Arithmetica 178 (2017), 87--100.

  84. A note on the quartic diophantine equation $A^4+hB^4=C^4+hD^4$, Notes on Number Theory and Discrete Mathematics 23 (2017), 1--3.

  85. A symmetric diophantine equation involving biquadrates, Notes on Number Theory and Discrete Mathematics 24 (2018), 140--144.

  86. A new method of solving certain quartic and higher degree diophantine equations, International Journal of Number Theory 14 (2018), 2129--2154.

  87. A diophantine problem on biquadrates revisited, The Mathematics Student 87 (2018), 129--132.

  88. (written jointly with J. Wroblewski) An Ancient Diophantine Equation with applications to Numerical Curios and Geometric Series, Colloq. Math. 151 (2018), 1--7.

  89. Symmetric diophantine systems and families of elliptic curves of high rank, Rocky Mountain Journal of Mathematics 49 (2019), 1419--1147.

  90. (written jointly with Andrew Bremner) The Fermat cubic and quartic curves over cyclic fields, Periodica Mathematica Hungarica 80 (2020), 147–157.

  91. Brahmagupta quadrilaterals with equal perimeters and equal areas, International Journal of Number Theory 16 (2020), 523–535.

  92. (written jointly with Arman Shamsi Zargar), A parametrised family of Mordell curves, Notes on Number Theory and Discrete Mathematics 26 (2020), 40–44.

  93. The Algebraic Solution of Unilateral Matrix Polynomial Equations, Serdica Mathematical Journal 45 (2020), 325–340.

  94. An improvement of Prouhet's 1851 result on multigrade chains, International Journal of Number Theory 16 (2020), 1425--1432.

  95. A diophantine system, Integers: Electronic Journal of Combinatorial Number Theory 20 (2020), Paper A27, 1--6.

  96. Four biquadrates whose sum is a perfect square, Journal of Integer sequences 24 (2021), Article 21.1.8, 7 pages.

  97. (written jointly with Arman Shamsi Zargar), A sextic diophantine chain and a related Mordell curve, Integers: Electronic Journal of Combinatorial Number Theory 21 (2021), 13 pages.

  98. (written jointly with Oliver Couto), A new diophantine equation involving fifth powers, Acta Arithmetica 202 (2022), 43--53.

  99. New solutions of the Tarry-Escott Problem of degrees 2, 3 and 5, Journal of Integer Sequences 24 (2021), Article 21.8.1, 8 pages.

  100. Cyclic pentagons and hexagons with integer sides, diagonals and areas, Serdica Mathematical Journal 46 (2020), 307--322.

  101. (written jointly with Iliya Bluskov and Alexander James), A diophantine equation inspired by Brahmagupta's identity, International Journal of Number Theory 18 (2022), 905--911.

  102. (written jointly with Arman Shamsi Zargar), Pairs of equiperimeter and equiareal triangles whose sides are perfect squares, Functiones et Approximatio 66 (2022), 245–251.