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## Homework Statement

:[/B]Determine whether there exists an integer x such that x^2 + 10 is a perfect square.

## Homework Equations

:[/B]N/A

## The Attempt at a Solution

:[/B]Assume x^2 + 10 = k^2 (a perfect square).

Solve for x in terms of k:

x = ±sqrt(k^2 - 10)

Since k is an integer and k^2 - 10 > 0, k > sqrt(10) > 3.

From here (and multiple other approaches), I'm not sure how to continue. Any help in proving whether such an integer value of x exists would be appreciated.