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P=m^{2003}n^{2017}-m^{2017}n^{2003} divisible by 24,7 (HOMC 2017 S Q14)

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September 8, 2019
divisiblenumber theory

Problem Statement

Put P=m2003n2017−m2017n2003P = m^{2003}n^{2017} - m^{2017}n^{2003} , where m,n∈Nm, n \in N. a) Is PP divisible by 2424? b) Do there exist m,n∈Nm, n \in N such that PP is not divisible by 77?
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