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n = d^3 + m^3 , m | n, d is the smallest divisor of n greater than 1

Source: 2022 Dutch IMO TST 1.1

December 3, 2022
number theoryDiophantine equationdiophantine

Problem Statement

Determine all positive integers n≥2n \ge 2 which have a positive divisor m∣nm | n satisfying n=d3+m3.n = d^3 + m^3. where dd is the smallest divisor of nn which is greater than 11.
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