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Question Number 100888 by bramlex last updated on 29/Jun/20

Find all pairs (k,n) of positive   integer for which 7^k −3^n  divides  k^4 +n^2  .

$${Find}\:{all}\:{pairs}\:\left({k},{n}\right)\:{of}\:{positive}\: \\ $$$${integer}\:{for}\:{which}\:\mathrm{7}^{{k}} −\mathrm{3}^{{n}} \:{divides} \\ $$$${k}^{\mathrm{4}} +{n}^{\mathrm{2}} \:. \\ $$

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