Two positive integers m and n are chosen such that m is the largest positive integer less than 100 with only two positive divisors and n is the smallest integer with exactly three positive divisors. What is m + n?

 May 18, 2022

Note that \(m\) is essentially the largest prime number less than 100. To find this, count down odd numbers from 100, and count how many factors they have.


Also note that \(n\) must be a perfect square, because that is the only way for a number to have 3 factors. 


Can you take it from here?

 May 18, 2022

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