MathDB

36

Part of 1962 AMC 12/AHSME

Problems(1)

Diophantine Equation

Source:

3/4/2010
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=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(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}