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p^m - q^3 = n^3

Source: Switzerland - 2013 Swiss MO Final Round p9

January 14, 2023
number theorydiophantineDiophantine equation

Problem Statement

Find all quadruples (p,q,m,n)(p, q, m, n) of natural numbers such that pp and qq are prime and the the following equation is fulfilled: pmāˆ’q3=n3p^m - q^3 = n^3
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