A is an integer to prove that 3A ^ 2 + 12a + 7 is not a complete square number

First of all, we must prove that the remainder of the square of integer a divided by 4 can only be 0 or 1. Because: a can only be odd or even. When a is even, let a = 2n. A ^ 2 = (2n) ^ 2 = 4N ^ 2, divide by 4 to 0. When a is odd, let a = 2n + 1. A ^ 2 = (2n + 1) ^ 2 = 4N ^ 2 + 4N + 1 = 4 (n ^ 2 + n) + 1

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