1. Prove that no square number leaves
remainder 2 when divided by 3.
[Hint: think of all integers as being
of the form 3n, 3n+1, 3n-1 and square them]
2. Prove that no square number
has remainder 2 or 3 when divided by 5.
Prove that no square number has remainder 3 or 5 when divided by 7.
4. Prove that every prime number greater than 3 can be written in the
form 6n+1 or 6n-1.
5. Prove that for every prime
number n, (n2 - 1)
/ 24 is an integer.
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