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1.

Part of 2019 Polish Junior MO Finals

Problems(1)

Two integers

Source: Polish Junior Math Olympiad 2019 Finals

10/23/2020
Let aa, bb be the positive integers greater than 11. Prove that if ab,  a−1b−1 \frac{a}{b},\; \frac{a-1}{b-1} differ by 1, then both are integers.
number theory