Hey all, I've got a few number theory exercises that are troubling me.(adsbygoogle = window.adsbygoogle || []).push({});

1. Prove a positive integer s is a square if and only if each of the exponents in its prime factorization is even.

2. Let c,d be positive, relatively prime integers. Prove that if cd is a square, c and d are squares.

3. Show that for four integers a,b,c,d, if a+b*sqrt(10)=c+d*sqrt(10), then a=c and b=d.

Hopefully someone can give me a start here. Thanks!

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# Homework Help: Number theory questions

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