1.) Show that (n+1)! = 2(n-1)! mod n+2(adsbygoogle = window.adsbygoogle || []).push({});

I finished this one. Actually very easy.

2.) Let n > 2 be odd. Prove that if 4[(n-1)! + 1] + n = 0 mod n(n+2) holds, then n, n+2 are twin primes. Hint says to use the previous problem.

I don't even know what to do for this problem.

3.) Prove the converse of the theorem in the preceeding problem is also true. Thus, the two problems together constitute a necessary and sufficient condition for (n, n+2) to be a pair of twin primes.

Obviously, if I can figure out #2, this one will be a walk in the park.

Thanks for any help given, I appreciate it.

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# 3 Problems

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