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Question

The numbers 16 and 25 are a pair of consecutive positive squares whose difference is 9. How many pairs of consecutive positive perfect squares have a difference of less than or equal to 2023?

Accepted Answer

Let x be the square root of the smaller of the two perfect squares. Then, (x+1)^2 - x^2 =x^2+2x+1-x^2 = 2x+1 2023. Thus, x 1011. So there are 1011 numbers that satisfy the equation.