Geodesic
Integers that are sums of two rational sixth powers
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 166-177

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DOI

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.
DOI : 10.4153/S0008439522000157
Mots-clés : Elliptic curve, Mordell–Weil sieve, Fermat curve, sixth power 
Newton, Alexis; Rouse, Jeremy. Integers that are sums of two rational sixth powers. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 166-177. doi: 10.4153/S0008439522000157
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     year = {2023},
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