3 years ago

On partitions into squares of distinct integers whose reciprocals sum to 1.

Max A. Alekseyev

In 1963, Graham proved that all integers greater than 77 (but not 77 itself) can be partitioned into distinct positive integers whose reciprocals sum to 1. He further conjectured that for any sufficiently large integer, it can be partitioned into squares of distinct positive integers whose reciprocals sum to 1. In this study, we establish the exact bound for existence of such representations by proving that 8542 is the largest integer with no such partition.

Publisher URL: http://arxiv.org/abs/1801.05928

DOI: arXiv:1801.05928v1

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