Prove that $$ N = \frac{5^{125} - 1}{5^{25} - 1} $$ is a composite number.
I just proved it will be a natural number with
quotient= $5^{100} +5^{75}+5^{50}+5^{25}+1$
But I do not know how to factorise it for proving it composite.
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Hint: try to factor the terms – Matti P. Feb 21 '20 at 12:55
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Ya , I tried but wasn't able to do – Aayush Feb 21 '20 at 12:56
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This is a repetition of this post: https://math.stackexchange.com/questions/2314779/prove-that-n-frac5125-1525-1-is-a-composite-number – Leo Feb 21 '20 at 13:04
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1How about you edit this question and include exactly what it is you don't understand? – Toby Mak Feb 21 '20 at 13:12
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By Aurifeuillean factorization, it's $(5^{50}+5^{38}+3\times5^{25}+5^{13}+1)(5^{50}-5^{38}+3\times5^{25}-5^{13}+1)$.
J. W. Tanner
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