If $a\equiv 62\pmod{99}$ and $b\equiv 75\pmod{99}$, then for what integer $n$ in the set $\{1000,1001,1002,\ldots,1097,1098\}$ is it true that $$a-b\equiv n\pmod{99}~?$$
Question:
If $a\equiv 62\pmod{99}$ and $b\equiv 75\pmod{99}$, then for what integer $n$ in the set $\{1000,1001,1002,\ldots,1097,1098\}$ is it true that $$a-b\equiv n\pmod{99}~?$$
Answer:
Let's think step by step.

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If $a\equiv 62\pmod{99}$ and $b\equiv 75\pmod{99}$, then for what integer $n$ in the set $\{1000,1001,1002,\ldots,1097,1098\}$ is it true that $$a-b\equiv n\pmod{99}~?$$
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