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If you have two consecutive integers then one of them must be odd and the other must be even.

The square of an odd integer must be odd, the square of an even integer must be even.

The sum of an odd number and an even number must be odd.

Thus, the sum of squares of any two consecutive numbers must be odd.

Therefore, the question has no valid answer.

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Q: What is the answer to this---Find two consecutive integers the sum of whose squares is 130?
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