Kieren MacMillan

### Questions (14)

 25 Is there an online encyclopedia of Diophantine equations (OEDE)? 17 Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$ 15 Are [Wieferich] primes the only solutions to the equation $2^{k-1} \equiv 1 \pmod{k^2}$? 12 Solving the quartic equation $r^4 + 4r^3s - 6r^2s^2 - 4rs^3 + s^4 = 1$ 11 A congruence conjecture regarding $(r-s)^4-1 \equiv 0\!\pmod{4r^2s}$

### Reputation (775)

 +20 Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$ +10 On integers as sums of three integer cubes revisited +10 prime factors of x^2 - 2 +10 Are [Wieferich] primes the only solutions to the equation $2^{k-1} \equiv 1 \pmod{k^2}$?

 3 Is (n,m)=(18,7) the only positive solution to n^2 + n + 1 = m^3 ? 3 On integers as sums of three integer cubes revisited 1 Does the Diophantine equation $(x^2+ay^2)(u^2+bv^2) = p^2+cq^2$ admit a complete solution? 1 Solving the quartic equation $r^4 + 4r^3s - 6r^2s^2 - 4rs^3 + s^4 = 1$

### Tags (11)

 7 diophantine-equations × 12 0 congruences × 2 6 nt.number-theory × 15 0 recurrences 1 quadratic-forms × 2 0 power-series 1 binary-quadratic-forms × 2 0 factorization 0 elementary-proofs × 5 0 generating-functions

### Bookmarks (1)

 12 Methods for solving Pell's equation?