Miraculous Solution To HARD Test Problem

Math
This one stumped me! This problem is part of the AIME, a qualifying test for the US Mathematical Olympiad team. The talented students who take the AIME only average about 20 percent–it’s a hard test! Plus no calculators are allowed. Can you figure out this problem from the 1987 test? Learn the trick which results in a miraculous solution. Thanks to all patrons! Special thanks this month to: Michael Anvari, Shrihari Puranik, Richard Ohnemus, Kyle.

Art of problem solving proof
https://artofproblemsolving.com/wiki/index.php/1987_AIME_Problems/Problem_14
Sophie Germain’s story is worth reading (the video has a hyphen in her name by mistake)
https://en.wikipedia.org/wiki/Sophie_Germain

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