FactorizationMethod Basic

Problem - 2483

How many integer solutions does the equation $(x+1)(y+1)=25$ have?

Because $25=5^2$, therefore $25$ has $3$ pairs of positive divisors, or $6$ pairs of negative divisors. Therefore, we have $$(x+1, y+1) = (\pm 1,\pm 25), (\pm 5, \pm 5), (\pm 25, \pm 1)$$

Therefore, the answer is $\boxed{6}$.