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Math Help - Help with proof

  1. #1
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    Help with proof

    If n^2+1 is prime, then n^2+1 can be expressed as 4k+1

    I was thinking you probably take n^2+1 and maybe do n^2+1=p and manipulate it from there?
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  2. #2
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    Quote Originally Posted by JSB1917 View Post
    If n^2+1 is prime, then n^2+1 can be expressed as 4k+1

    I was thinking you probably take n^2+1 and maybe do n^2+1=p and manipulate it from there?
    Unless I am missing something the statement is false.

    let n=1 \implies 1^2+1=2 is prime but there isn't an integer such that

    4k+1=2
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  3. #3
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    Quote Originally Posted by JSB1917 View Post
    If n^2+1 is prime, then n^2+1 can be expressed as 4k+1
    That is not true if n=1. Is it?
    2 is prime.
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  4. #4
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    sorry, I forgot to put n =/= 1.
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  5. #5
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    If n>0~\&~n^2+1 is a prime number, then it is odd.
    So n^2 is even. WHY?
    That means n is even, or n=2k for some k
    Therefore, n^2+1=4j+1 where j=k^2.
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