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Math Help - prove or disprove, induction

  1. #1
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    prove or disprove, induction

    n^2 - n + 41 is prime (try some examples), for all n is an element of N.
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  2. #2
    o_O
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    n=41?
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  3. #3
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    Quote Originally Posted by o_O View Post
    n=41?
    Let n=1
    12 - 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.

    Is this correct?
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  4. #4
    o_O
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    You can't use induction here. Induction is used to prove statements for all positive integers.

    Here, n^2 - n + 41 can be prime for some values of n (such as n = 1) or not prime (such as n = 41).

    To disprove a statement, all you need is just one single counterexample which I provided for you.
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