Difference between revisions of "2021 JMC 10 Problems/Problem 19"
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Latest revision as of 16:03, 1 April 2021
Problem
Two distinct divisors of are mutual if their difference divides their product. For instance, is mutual as Suppose a mutual pair exists where for a positive integer What is the sum of all possible
Solution
Observe that Because , it follows that . Since , we must also have . Note that we cannot have , because this will result in being neither a multiple of nor . Thus, we need only to check and Note that must be of the form for non-negative integers and so our desired answer is .