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:

Let $p$ and $q$ be distinct prime numbers.
Then, let $(\log_{10}q)^5=\sin^2p+\cos^2p$ , where $p$ is in degrees.
Find all pairs $(p,q)$ satisfying the above conditions.
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?

Problem created correctly, solution incorrectly Problem created correctly, solution created correctly Problem created incorrectly, solution also incorrect Problem created incorrectly, however solution is correct

1 solution

Anandmay Patel
Aug 3, 2016

The problem is very much created correctly. But the correct solution is,there exist 0 such pairs. No doubt p can take infinite values to make the RHS of the equation as 1,but this will always make the value of q=10,not a prime number.

A geometry problem by Anandmay Patel

1 solution

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