A and B

$\frac ab=c=a-1$

${\color{#3D99F6}b=\frac a{a-1}}$

$\frac ab=a-1$

$a=ab-b$

$a(b-1)=b$

${\color{#3D99F6}a=\frac b{b-1}}$

The blue expressions are symmetrical and can be satisfied with $a=b=2$

Giving that c is a whole number, the only two possible cases is a>b or a=b. If a>b in order for c to be a whole number, a must be a multiple of b, or a=kb, where k is another whole number. But this implies that c=k, and hence k+1=a=kb, which leads to k=1/(b-1), a clearly contradiction, since k must be a whole number. If a=b Then we have c=1, a=2 and b=2, all of them being whole numbers. Therefore, a=b is the correct answer.