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AMO · 2027 · Grades 6-7 · Self-study SET 24 Question 10

AMO

Question 10

Find the smallest integer which, when divided by 7, gives a remainder of 0, but when divided by 10 gives a remainder of 1.

Editorial clarification: in this self-study version, seek the smallest positive integer. Over all signed integers, the original wording has no smallest solution.

**Input:** Enter the integer only, without units.