# The number of integer pairs (x,y) satisfy the equation x(x+1)=2^y is?

If $x$ is an intger then $x \left(x + 1\right)$ is a product of two consecutive integers . One of which is odd and other is even. Again the ${2}^{y}$,where $y$ is an integer has the values $2 , 4 , 8 , 16. . .$.
So ${2}^{y}$ has no multiple of odd intger other than 1.
Hence the given relation $x \left(x + 1\right) = {2}^{y}$ is satisfied only when $x = 1 \mathmr{and} y = 1$.