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Finding a Number That Meets Specific Divisibility Conditions

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math
Find a number that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a remainder of 2, when divided by 4 leaves a remainder of 3, when divided by 5 leaves a remainder of 4, when divided by 6 leaves a remainder of 5, but when divided by 7 leaves no remainder.

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

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