- #1
mbcsantin
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Homework Statement
For all n is an element of N, n2 - n + 41 is prime
N= natural numbers
Homework Equations
None.
The Attempt at a Solution
Let n=1
12 - 1 + 41 = 41 is prime.
n2 - n + 41 is not prime. so this hypothesis is not correct.
assume n2 - n + 41 is not prime. there exist n that let n2 - n + 41 = n2 so n2 - n + 41 is not prime.
therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n2 - n + 41 is not prime.
Hence n2 - n + 41 not true for all n is an element of N.