SOLUTION: Prove that a squared = 0 or 1 mod 3 for all a∈ Integers
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Question 479798: Prove that a squared = 0 or 1 mod 3 for all a∈ Integers
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!
Set up 3 cases for a:
a = 3n
a = 3n+1
a = 3n+2
where n represents any integer
Case 1:
Divide by 3
Remainder is 0 for all n
Case 2:
Divide by 3
Remainder is 1 for all n
Case 3:
Divide by 3
Remainder is 1 for all n
Therefore a^2 = 0 or 1 mod 3 for all a (integers)
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