MathDB
P02 [Number Theory] - Turkish NMO 1st Round - 2013

Source:

April 17, 2013
modular arithmeticnumber theoryprime numbers

Problem Statement

How many triples (p,q,n)(p,q,n) are there such that 1/p+2013/q=n/51/p+2013/q = n/5 where pp, qq are prime numbers and nn is a positive integer?
<spanclass=latexbold>(A)</span> 7<spanclass=latexbold>(B)</span> 6<spanclass=latexbold>(C)</span> 5<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 6 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 4