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(n-1)^2<=x<(n+1)^2 set

Source: 2001 Moldova MO Grade 7 P7

April 12, 2021
setnumber theory

Problem Statement

Let nn be a positive integer. We denote by SS the sum of elements of the set M={x∈N∣(n−1)2≤x<(n+1)2}M=\{x\in\mathbb N|(n-1)^2\le x<(n+1)^2\}. (a) Show that SS is divisible by 66. (b) Find all n∈Nn\in\mathbb N for which S+(1−n)(1+n)=2001S+(1-n)(1+n)=2001.
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