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PAMO Problem 2: Product and sum of primes

Source: 2019 Pan-African Mathematics Olympiad, Problem 2

April 9, 2019
number theoryprime numbersSums and ProductsPAMO

Problem Statement

Let kk be a positive integer. Consider kk not necessarily distinct prime numbers such that their product is ten times their sum. What are these primes and what is the value of kk?
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