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Turkey NMO 2006 1st Round - P34 (Number Theory)

Source:

February 3, 2013

Problem Statement

How many positive integers less than 10001000 are there such that they cannot be written as sum of 22 or more successive positive integers?
<spanclass=latexbold>(A)</span> 6<spanclass=latexbold>(B)</span> 10<spanclass=latexbold>(C)</span> 26<spanclass=latexbold>(D)</span> 68<spanclass=latexbold>(E)</span> 72 <span class='latex-bold'>(A)</span>\ 6 \qquad<span class='latex-bold'>(B)</span>\ 10 \qquad<span class='latex-bold'>(C)</span>\ 26 \qquad<span class='latex-bold'>(D)</span>\ 68 \qquad<span class='latex-bold'>(E)</span>\ 72