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Sum of Consecutive Integers Dividing 6n

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January 12, 2009

Problem Statement

For how many positive integers n n does 1 \plus{} 2 \plus{} \cdots \plus{} n evenly divide from 6n 6n? <spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 11 <span class='latex-bold'>(A)</span>\ 3\qquad <span class='latex-bold'>(B)</span>\ 5\qquad <span class='latex-bold'>(C)</span>\ 7\qquad <span class='latex-bold'>(D)</span>\ 9\qquad <span class='latex-bold'>(E)</span>\ 11
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