MathDB

22

Part of 2008 National Olympiad First Round

Problems(1)

Turkey NMO 2008 1st Round - P22 (Number Theory)

Source:

8/26/2012
How many pairs of postive integers (a,b)(a,b) with a≥ba\geq b are there such that a2+b2a^2+b^2 divides both a3+ba^3+b and a+b3a+b^3?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<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>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}