perfect sqare leave a remainder of 0 and 1 when divided by 7
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The remainder upon dividing by 7 will then be modulo 7. 0,1,4,2,2,4,1. Therefore the remainder upon dividing a perfect square by 7 can only take the values 0,1,2,4 unlike other integers that can also take the values 3,5,6.
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A perfect square leaves a remainder 0 or 1 when divisible by
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