Here are my 3 problems:

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Prove or disprove that (n^2)-1 is composite whenever n is a positive integer greater than 1

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Prove that (a mod m)(b mod m) mod m = ab mod m for all integers a and b whenever m is a positive integer.

Quote:

Prove or disprove that a mod m + b mod m = (a + b) mod m for all integers a and b whenever m is a positive integer.

Help to Any of these would be appreciated..

thanks