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2023 SSMO Relay Round 5 Problems/Problem 3

Revision as of 21:30, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that <math>x^2+y^2 = N.</math> Find the remainder when the expected value of the square of the maximum value <math>ax+by</math>...")
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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 $\{1,2,\dots,N\}.$

Solution

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