MathDB

26

Part of 1998 National Olympiad First Round

Problems(1)

y = sqrt( x +1988 and so on)

Source: 0

4/23/2009
How many ordered integer pairs (x,y) \left(x,y\right) are there satisfying following equation: y \equal{} \sqrt{x\plus{}1998\plus{}\sqrt{x\plus{}1998\plus{}\sqrt{x\plus{}1997\plus{}\sqrt{x\plus{}1997\plus{}\ldots \plus{}\sqrt{x\plus{}1\plus{}\sqrt{x\plus{}1\plus{}\sqrt{x\plus{}\sqrt{x} } } } } } } }.
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 1998<spanclass=′latex−bold′>(D)</span> 3996<spanclass=′latex−bold′>(E)</span> Infinitely many<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 1998 \qquad<span class='latex-bold'>(D)</span>\ 3996 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}