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2013 preRMO p14, min odd m such 1+ 2 +...+ m square of an integer

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August 8, 2019
number theoryPerfect SquaresPerfect Square

Problem Statement

Let mm be the smallest odd positive integer for which 1+2+...+m1+ 2 +...+ m is a square of an integer and let nn be the smallest even positive integer for which 1+2+...+n1 + 2 + ... + n is a square of an integer. What is the value of m+nm + n?
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