MathDB
Diophantine Equation

Source:

March 4, 2010

Problem Statement

If both x x and y y are both integers, how many pairs of solutions are there of the equation (x\minus{}8)(x\minus{}10) \equal{} 2^y? <spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> more than 3 <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{more than 3}