AMC 10 Step by Step
2021 AMC Fall 10BProblem 22P21-25~8 minPrint

For each integer n2n\geq 2 , let SnS_n be the sum of all products jkjk , where jj and kk are integers and 1j<kn1\leq j<k\leq n . What is the sum of the 10 least values of nn such that SnS_n is divisible by 33 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.