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March 29, 2017

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What is the largest prime factor of 5^8 +2^2 ?

  • Algebra - ,

    5^8 + 2^2
    = 25^4 + 2^2
    = 625^2 + 2^2
    = (625 + 2)^2 - 2(2)(625)
    = 627^2 - (2(25))^2 . a difference of squares
    = 627^2 - 50^2
    = (627 + 50)(627-50)
    = 677(577)

    both of these are primes, so the largest prime factor is 677

    check:
    5^8 + 2^2 = 390629 and 390629/677 = 577

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