Almost universal mixed sums of squares and polygonal numbers

2018/01/01 by Wu, Hai-Liang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.00440

Abstract

For each integer m≥3, let P_m(x) denote the generalized m-gonal number ((m-2)x²-(m-4)x)/(2) with x∈ℤ. Given positive integers a,b,c,k and an odd prime number p with p\nmid c, we employ the theory of ternary quadratic forms to determine completely when the mixed sum ax²+by²+cP_p^k+2(z) represents all but finitely many positive integers.

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