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Hard products... jk

Source: AMC 10B (Fall) Problem 22

November 17, 2021
AMCAMC 10AMC 10 BalgebraSummation2021 AMC Fall

Problem Statement

For each integer n≥2 n\geq 2 , let Sn S_n be the sum of all products jk jk , where j j and k k are integers and 1≤j<k≤n 1\leq j<k\leq n . What is the sum of the 10 least values of n n such that Sn S_n is divisible by 3 3 ? <spanclass=′latex−bold′>(A)</span>196<spanclass=′latex−bold′>(B)</span>197<spanclass=′latex−bold′>(C)</span>198<spanclass=′latex−bold′>(D)</span>199<spanclass=′latex−bold′>(E)</span>200<span class='latex-bold'>(A) </span>196\qquad<span class='latex-bold'>(B) </span>197\qquad<span class='latex-bold'>(C) </span>198\qquad<span class='latex-bold'>(D) </span>199\qquad<span class='latex-bold'>(E) </span>200
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