6th Grade Perfect Squares: Problem 2

Problem: The number S = (1x2x3x…xn) + (4k+3), with n being greater than or equal to 3, and k is an integer from 1 to 100. How many different values of k allows S to be a positive integer perfect square?

Key: Perfect squares can only get a remainder of 0 or 1 when divided by 4 and/or 3

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