Science:Math Exam Resources/Courses/MATH220/December 2011/Question 08
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Question 08 

Prove that if p is a prime number and p > 4, then 
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Hint 

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By saying that we look at primes larger than 4, what we really mean is we look at all the primes except 2 and 3 (which makes sense since 2^{2} = 4 and 3^{2} = 9 which is 3 mod 6; so these two don't work anyway). Now any prime p other than 2 and 3 will then clearly NOT be a multiple of two and NOT be a multiple of 3. This means that since integers that are 0, 2 or 4 mod 6 are all even and since an integer that is 3 mod 6 is a multiple of 3. But since and we can conclude that if p is a prime larger than 4, then its square is always 1 mod 6. 