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2024 SSMO Relay Round 5 Problems/Problem 3

Problem

Let $T = TNYWR.$ Let $k$ be the maximum prime factor that divides $T.$ How many values of $x$ satisfy both $\sin x^2+\cos x^2=\sin^2 x + \cos^2 x$ and $-k \le x \le k?$

Solution

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