cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A212420 Known primes such that there are no pairwise coprime solutions to the Diophantine equation of the form x^3 + y^3 = p^a z^n with a >= 1 an integer and n >= p^(2p) prime.

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%I A212420 #18 Jul 14 2019 06:28:46
%S A212420 53,83,149,167,173,199,223,227,233,263,281,293,311,347,353,359,389,
%T A212420 401,419,443,449,461,467,479,487,491,563,569,571,587,599,617,641,643,
%U A212420 659,719,727,739,743,751,809,811,823,827,829,839,859,881,887,907,911,929,941,947,953,977,983
%N A212420 Known primes such that there are no pairwise coprime solutions to the Diophantine equation of the form x^3 + y^3 = p^a z^n with a >= 1 an integer and n >= p^(2p) prime.
%C A212420 These primes are the prime numbers p greater than 3 such that for every elliptic curves with conductor of the form 18p, 36p, or 72p we have that 4 does not divide the order of the torsion subgroup over the rationals but at least one curve with 2 dividing this order, such that there is a prime q congruent to 1 modulo 6 such that 4 does not divide the order of the torsion subgroup over the finite field of size q.
%H A212420 M. A. Bennett, F. Luca and J. Mulholland, <a href="http://www.labmath.uqam.ca/~annales/volumes/35-1/PDF/001-015.pdf">Twisted extensions of the cubic case of Fermat's Last Theorem</a>, Ann. Sci. Math. Quebec. 35 (2011), 1-15.
%K A212420 nonn,obsc
%O A212420 1,1
%A A212420 _Carmen Bruni_, May 15 2012