We are looking for two consecutive integers whose squares sum up to 41. A consecutive integer means that one integer comes directly after the other, or is just added to 1. Since 16+25=41 , our two numbers must be 4 and 5.
n^2 + (n+1)^2 = 41
n^2 + n^2 + 2n + 1 = 41
2n^2 + 2n -40 = 0
n = 4 and n=-5
4^2 + 5^2 = 41 correct
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-5^2 + -4^2 = 41 correct
So, the integers are 4 and 5 AND -4 and -5
