Competition problem — Number theory

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Number theory Difficulty 5.0 AIME, harder Find the answer

5. What is the least number greater than 1992 that gives a remainder of $7$ when divided by $9$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

5. Divide 1992 by 9 with a remainder

We obtained a remainder of 3. To make the remainder equal to 7, the divisor needs to be increased by four:

$1992+4=1996 \text {. }$

Answer: 1996.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.