smc

We are given these congruences: $1059\equiv r(\mathrm{mod}d)$ (i) $1417\equiv r(\mathrm{mod}d)$ (ii) $2312\equiv r(\mathrm{mod}d)$ (iii) Let's make a new congruence by subtracting (i) from (ii), which results in $$358\equiv 0(\mathrm{mod}d).$$ Subtract (ii) from (iii) to get $$895\equiv 0(\mathrm{mod}d).$$ Now we know that $358$ and $895$ are both multiples of $d$. Their prime factorizations are $358=2\cdot 179$ and $895=5\cdot 179$, so their common factor is $179$, which means $d=179$. Plug $d=179$ back into any of the original congruences to get $r=164$. Then, $d-r=179-164=\boxed{15}$.