2023 SSMO Relay Round 5 Problems/Problem 3

Problem

Let $T=TNYWR$ . Suppose that $x^2+y^2 = N.$ Find the remainder when the expected value of the square of the maximum value $ax+by$ is divided by $100,$ where $a$ and $b$ distinct members from the set $\{1,2,\dots,N\}.$

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2023 SSMO Relay Round 5 Problems/Problem 3

Problem

Solution