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P10 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 17, 2013
number theoryrelatively prime

Problem Statement

How many positive integers nn are there such that there are exactly 2020 positive odd integers that are less than nn and relatively prime with nn?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 4<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 2<spanclass=latexbold>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}