On sums of primes and triangular numbers

Details On sums of primes and triangular numbers On sums of primes and triangular numbers

2008-03-26

arxiv.org/abs/0803.3737v7

Journal of Combinatorics and Number Theory 1(2009), no.1, 65-76

Mathematics

Number Theory

Scientific paper

We study whether sufficiently large integers can be written in the form cp+T_x, where p is either zero or a prime congruent to r mod d, and T_x=x(x+1)/2 is a triangular number. We also investigate whether there are infinitely many positive integers not of the form (2^ap-r)/m+T_x with p a prime and x an integer. Besides two theorems, the paper also contains several conjectures together with related analysis and numerical data. One of our conjectures states that each natural number not equal to 216 can be written in the form p+T_x with x an integer and p a prime or zero; another conjecture asserts that any odd integer n>3 can be written in the form p+x(x+1) with p a prime and x a positive integer.

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