Edward Norton Lorenz. 23 May 1917 — 16 April 2008

20 May 2001 − − 1917

Functional and Logic Programming, 9th International Symposium, FLOPS 2008, Ise, Japan, April 14-16, 2008. Proceedings

Cover Vol 16, No. 2, April 2019

The Contragredient April 16

2 00 8 Preprint ( April 23 , 2008 ) MIXED SUMS OF SQUARES AND TRIANGULAR NUMBERS ( III )

In this paper we prove a conjecture of Sun which states that each positive integer is a sum of a square, an odd square and a triangular number. Given any positive integer m, we show that p = 2m + 1 is a prime congruent to 3 mod 4 if and only if Tm = m(m + 1)/2 cannot be expressed as a sum of two odd squares and a triangular number, i.e., p = x + 8(y + z) for no odd integers x, y, z. We also sho...