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Can you find a square number that when divided by 3 has a remainder of 2?
Wiki User
∙ 14y ago
No because it is impossible.
Let mod(x.3) denote the remainder when x is divided by 3. Let n be any integer. Then mod(n,3) = 0,1 or 2.
When mod(n,3) = 0, mod(n2,3) = 0
When mod(n,3) = 1, mod(n2,3) = 1
When mod(n,3) = 2, mod(n2,3) = 4 and, equivalently mod(n2,3) = 1.
So, there are no integers whose squar leaves a remainder of 2 when divided by 3.
Wiki User
∙ 14y ago
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