Total number of integer ordered pairs that satisfy the difference between Arithmetic mean and Geometric mean is 1

Posted on June 25, 2024 by Sumant Sumant

Suppose (a,b) are non negative integers such that\frac{a+b}{2}-2\sqrt{ab}=1 and 0\le a,b \le 100. Find the number of ordered pairs that satisfy the above condition. (Australian Mathematical Olympiad, 2020)

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