Algebra Prime Time

 The Problems:

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.

 3.  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. 

[Hint: use result from 4]

 

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Last modified: June 18, 2007