MathDB

35

Part of 2001 National Olympiad First Round

Problems(1)

P35 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

4/23/2014
How many ordered pairs (p,n)(p,n) are there such that (1+p)n=1+pn+np(1+p)^n = 1+pn + n^p where pp is a prime and nn is a positive integer?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 0<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 5 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 1 \qquad<span class='latex-bold'>(D)</span>\ 0 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}