Number of solutions for (a-x)(b-y)-1=0

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How to find number of integer solutions for x and y for given values of a and b . is it related to number of divisors , i read it from a post bit didn't get it . Anybody can explain with example .

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The product $(a-x)(b-y)$ is $1$ iff $a-x=b-y=\pm1$, so you get two solutions.