MathDB
Turkey NMO 2006 1st Round - P22 (Number Theory)

Source:

February 2, 2013
modular arithmetic

Problem Statement

How many integer pairs (x,y)(x,y) are there such that 0\leq x < 165,   0\leq y < 165 \text{ and } y^2\equiv x^3+x \pmod {165}? <spanclass=latexbold>(A)</span> 80<spanclass=latexbold>(B)</span> 99<spanclass=latexbold>(C)</span> 120<spanclass=latexbold>(D)</span> 315<spanclass=latexbold>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 80 \qquad<span class='latex-bold'>(B)</span>\ 99 \qquad<span class='latex-bold'>(C)</span>\ 120 \qquad<span class='latex-bold'>(D)</span>\ 315 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}