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.

53, 83, 149, 167, 173, 199, 223, 227, 233, 263, 281, 293, 311, 347, 353, 359, 389, 401, 419, 443, 449, 461, 467, 479, 487, 491, 563, 569, 571, 587, 599, 617, 641, 643, 659, 719, 727, 739, 743, 751, 809, 811, 823, 827, 829, 839, 859, 881, 887, 907, 911, 929, 941, 947, 953, 977, 983

Offset: 1

Author

Carmen Bruni, May 15 2012

Keywords

• nonn
• obsc

Comments

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.

Links

• M. A. Bennett, F. Luca and J. Mulholland, Twisted extensions of the cubic case of Fermat's Last Theorem, Ann. Sci. Math. Quebec. 35 (2011), 1-15.