# A geometry problem by Anandmay Patel

Geometry Level pending

Jim tries to create a logarithmic-trigo problem. He takes the following steps to create the problem:

1. Let $$p$$ and $$q$$ be distinct prime numbers.
2. Then, let $$(\log_{10}q)^5=\sin^2p+\cos^2p$$, where $$p$$ is in degrees.
3. Find all pairs $$(p,q)$$ satisfying the above conditions.
4. According to him, there are infinite such pairs, as $$p$$ can take infinite values to make the RHS of the equation equal to 1.

Has he created the problem with the solution correctly?

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