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p^m=(a^6 + 21a^4b^2 + 35a^2b^4 + 7b^6) (b^6 + 21b^4a^2 + 35b^2a^4 + 7a^6)

Source: 2016 Latvia BW TST P20

December 17, 2022
power of primePerfect PowersPerfect powernumber theory

Problem Statement

For what pairs of natural numbers (a,b)(a, b) is the expression (a6+21a4b2+35a2b4+7b6)(b6+21b4a2+35b2a4+7a6)(a^6 + 21a^4b^2 + 35a^2b^4 + 7b^6) (b^6 + 21b^4a^2 + 35b^2a^4 + 7a^6) the power of a prime number?
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