MathDB

2

Part of 2009 National Olympiad First Round

Problems(1)

a^2 + b^4 = 5^n

Source: 0

4/28/2009
If a,b,n a,b,n are positive integers, number of solutions of the equaition a^2 \plus{} b^4 \equal{} 5^n is
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> Infinitely many<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinitely many}