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Prove that

n^4+4 prime number <==> n=1

Note by Mouataz Chadmi
3 years, 5 months ago

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\( n^4 + 4 = (n^2-2n+2)(n+2n+2)\) So the expression \( n^4+4\) can be factored for every \(n > 1\) and hence it can never be a prime for \(n>1\) Vikram Waradpande · 3 years, 5 months ago

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@Vikram Waradpande That's not complete, you should mention that \(n^2-2n+2=1 \implies (n-1)^2=0 \implies n = 1\), and if \(n>1\), then both factors are bigger than \(1\), hence \(n^4+4\) is not prime. Tim Vermeulen · 3 years, 5 months ago

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@Tim Vermeulen Oh yeah, forgot that! That's why you're on level 5 and i'm on 4! Vikram Waradpande · 3 years, 5 months ago

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