1. The problem statement, all variables and given/known data: Determine whether there exists an integer x such that x^2 + 10 is a perfect square. 2. Relevant equations: N/A 3. The attempt at a solution: 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.