MathDB

10

Part of 2008 National Olympiad First Round

Problems(1)

Turkey NMO 2008 1st Round - P10 (Number Theory)

Source:

8/25/2012
How many pairs of positive integers (x,y)(x,y) are there such that xy−71x+30=0\sqrt{xy}-71\sqrt x + 30 = 0?
<spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 72<spanclass=′latex−bold′>(D)</span> 2130<spanclass=′latex−bold′>(E)</span> Infinitely many <span class='latex-bold'>(A)</span>\ 8 \qquad<span class='latex-bold'>(B)</span>\ 18 \qquad<span class='latex-bold'>(C)</span>\ 72 \qquad<span class='latex-bold'>(D)</span>\ 2130 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}