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Proving that a number is divisible by 4th Fermat prime F_4

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January 3, 2011
number theory unsolvednumber theory

Problem Statement

Prove that the number 191976+76197619^{1976} + 76^{1976}: (a)(a) is divisible by the (Fermat) prime number F4=224+1F_4 = 2^{2^4} + 1; (b)(b) is divisible by at least four distinct primes other than F4F_4.
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