On the largest size of a partition that is both s-core and t-core

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Let s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane and Sze regarding the largest size of a partition that is simultaneously s-core and t-core by solving an equivalent problem concerning sets S of positive integers with the property that for n∈S, n−s∈S whenever n?s and n−t∈S whenever n?t.

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