“Everything has beauty, but not everyone can see it.” - Confucius Index
Part 3. Quadratic Polynomial as a kth Power 5) May (none) 11) November (see Article 7)
6) June 12) December (see Articles 8-11)
(Pls read first: This almost 300-page book is divided into more than 30 sections. For navigation, note that the topic with a link, and those immediately below it without a link, belong to the same section. Alternatively, one can use the Home and other buttons on the sidebar. For questions and comments, feel free to email author at tpiezas@gmail.com.)
Part 0. Introduction (Link 0)
Part 1. Assorted Identities (Link 1)
Part 2. Sums of Squares (Link 2) I. Sums of two squares
IV. Some Identities of Squares (Link 5b)
Part 3. Quadratic Polynomial as a kth Power (Link 6)
I. Univariate: ax2+bx+c = z2
II. Bivariate: ax2+bxy+cy2 = zk
III. Bivariate: ax2+bxy+cy2 = dz2
PART 4. Simultaneous Polynomials Made Squares (Link 7)
I. Two variables
II. Three variables
III. Four variables
PART 5. Pell Equations (Link 8)
I. Complete Solution II. Transformations III. Polynomial Parametrizations
IV. Diophantine Equations needing Pell Equations (Link 9)
PART 6. Third Powers (Link 10)
I. Sums of cubes
II. Cubic polynomials as kth powers
A. Univariate: ax3+bx2+cx+d2 = tk
B. Bivariate: ax3+bx2y+cxy2+dy3 = tk
PART 7. Fourth Powers (Link 13)
I. Sums of biquadrates
12.1 a+b = nc; d+e = nf (Link 15) 12.2 a+b ≠ c; d+e ≠ f 12.3 a+b±c = n(d+e±f) (Link 16) 12.4 na+b+c = d+e+nf 12.5 na+b = e+nf 12.6 a+d = n(c+f) 12.7 (a2-f2)c2 = -(b2-e2)d2
II. Quartic Polynomials as kth Powers (Link 18)
PART 8. Fifth Powers
I. General Conjectures and Problems (Link 19) II. Some Theorems on Equal Sums of Like Powers III. Fifth Powers (Link 20) 5.1 Four terms 5.2 Six terms 5.3 Seven terms (Link 21) 5.4 Eight terms (Link 22) 5.5 Ten terms 5.6 Twelve terms
PART 9. Sixth Powers (Link 23)
6.1 Four terms 6.2 Six terms 6.3 Seven terms (Link 24) 6.4 Eight terms (Link 25)
PART 10. Seventh Powers (Link 26)
7.1 Eight terms 7.2 Nine terms 7.3 Ten terms (Link 27)
PART 11. Eighth Powers (Link 28)
8.1 Eight terms
8.2 Nine terms
8.3 Ten terms
8.4 Twelve terms
8.5 Fourteen terms 8.6 Sixteen terms
8.7 Seventeen terms
PART 12. Ninth Powers (Link 29)
PART 13. Tenth Powers (Link 30) PART 14. Eleventh and Higher Powers (Link 31)
PART 15. Index of Updates (Link)
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