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A317244 For n >= 3, smallest prime number N such that for every prime p >= N, every element in Z_p can be expressed as a sum of two n-gonal numbers mod p, without allowing zero as a summand.

%I A317244 #15 Jul 17 2021 07:28:19
%S A317244 11,11,11,11,11,11,11,11,11,11,11,13,11,11,11,11,11,11,11,23,11,11,13,
%T A317244 29,11,11,11,11,11,11,11,37,11,13,11,11,11,11,23,11,11,11,11,47,13,11,
%U A317244 29,53,11,11,11,11,11,11,11,13,11,23,11,61,11,11,37,11,11,11,13,71,11,29,11,73,11,11,11,11,23,13,11,83,11,11,11,89,11,11,47,11,13,11,11,11,29,37,53,23,11
%N A317244 For n >= 3, smallest prime number N such that for every prime p >= N, every element in Z_p can be expressed as a sum of two n-gonal numbers mod p, without allowing zero as a summand.
%H A317244 Joshua Harrington, Lenny Jones, and Alicia Lamarche, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Jones/jones14.html">Representing Integers as the Sum of Two Squares in the Ring Z_n</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.4.
%H A317244 Bernard M. Moore and H. Joseph Straight, <a href="https://www.jstor.org/stable/48568142">Pythagorean triples in multiplicative groups of prime power order</a>, Pi Mu Epsilon Journal, vol. 14, no. 3, 2015, pp. 191-198.
%K A317244 nonn
%O A317244 3,1
%A A317244 _Theresa Baren_, _James Hammer_, _Joshua Harrington_, _Ziyu Liu_, _Sean E. Rainville_, Melea Roman, _Hongkwon V. Yi_, Jul 24 2018