Integers that are sums of two rational sixth powers. Issue 1 (7th March 2023) - Newton, Alexis; Rouse, Jeremy
Abstract: We prove that 164 634 913 is the smallest positive integer that is a sum of two rational sixth powers, but not a sum of two integer sixth powers. If C_k is the curve x^6 + y^6 = k, we use the existence of morphisms from C_k to elliptic curves, together with the Mordell–Weil sieve, to rule out the existence of rational points on C_k for various k .