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 Post subject: primes of the form 4k+1Posted: Sat, 2 Jun 2012 15:44:42 UTC

Joined: Sat, 2 Jun 2012 15:31:17 UTC
Posts: 8
Prove that if is a prime number of the form then there are integers such that .

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 Post subject: Re: primes of the form 4k+1Posted: Sat, 2 Jun 2012 15:54:50 UTC
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m2012 wrote:
Prove that if is a prime number of the form then there are integers such that .

Units of .

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 Post subject: Re: primes of the form 4k+1Posted: Sat, 2 Jun 2012 16:01:06 UTC

Joined: Sat, 2 Jun 2012 15:31:17 UTC
Posts: 8

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 Post subject: Re: primes of the form 4k+1Posted: Sat, 2 Jun 2012 20:46:50 UTC
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m2012 wrote:

Then perhaps you should explain your background and what you have tried on this problem so we know what level of answer is appropriate for your abilities.

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 Post subject: Re: primes of the form 4k+1Posted: Sun, 3 Jun 2012 10:43:04 UTC

Joined: Sat, 2 Jun 2012 15:31:17 UTC
Posts: 8
Would you please show me the idea of elementary proof, without quadratic integer rings theory or Pell's equatioion. I know congruences theory, for example

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