For discussing Olympiad Level Number Theory problems
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Unread post by mathlover007 » Wed Jan 03, 2018 9:04 pm

Prove that any integer of the form ( 4k + 3 ) has a prime factor of the same form .

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Re: Divisibility

Unread post by samiul_samin » Thu Mar 01, 2018 8:36 pm

Any prime number greater than $2$ is in form $4k+1$ or $4k+3$.
So,if we multiply some $4k+1$ type primes,we will get 4k+1 type compsite number.So,we will get a $4k+3$ type integer if at least one prime factor of it is in $4k+3$ form.
So,we are done.

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