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Part of 2013 National Olympiad First Round

Problems(1)

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

Source:

4/17/2013
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=′latex−bold′>(A)</span> 7<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(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
modular arithmeticnumber theoryprime numbers