MathDB

18

Part of 2005 National Olympiad First Round

Problems(1)

P18 [Number Theory] - Turkish NMO 1st Round - 2005

Source:

10/26/2013
How many integers 0≤x<1210\leq x < 121 are there such that x5+5x2+x+1≡0(mod121)x^5+5x^2 + x + 1 \equiv 0 \pmod{121}?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <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>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 5
modular arithmeticquadratics