(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For all n is an element of N, n^{2}- n + 41 is prime

N= natural numbers

2. Relevant equations

None.

3. The attempt at a solution

Let n=1

1^{2}- 1 + 41 = 41 is prime.

n^{2}- n + 41 is not prime. so this hypothesis is not correct.

assume n^{2}- n + 41 is not prime. there exist n that let n^{2}- n + 41 = n^{2}so n^{2}- n + 41 is not prime.

therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n^{2}- n + 41 is not prime.

Hence n^{2}- n + 41 not true for all n is an element of N.

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# Homework Help: Prove or disprove, induction

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