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all integer solutions to m^{m+n} = n^{12} and n^{m+n} = m^3

Source: Vietnamese MO (VMO) 1976 P1

August 20, 2018
system of equationsnumber theoryInteger sequenceinteger equation

Problem Statement

Find all integer solutions to mm+n=n12,nm+n=m3m^{m+n} = n^{12}, n^{m+n} = m^3.
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