On the existence of Graham partitions with congruence conditions

초록

In 1963, Graham introduced a problem to find integer partitions such that the reciprocal sum of their parts is 1. Inspired by Graham's work and classical partition identities, we show that there is an integer partition of a sufficiently large integer $n$ such that the reciprocal sum of the parts is $1$, while the parts satisfy certain congruence conditions.

키워드