(a

^{3}b + 1)/(a + 1) and (b

^{3}a + 1)/(b – 1)

are both positive integers.

From the Junior Balkan Mathematical Olympiad 2013

My apologies, but the above question has a typo! The

*actual*question is the following.

**Find all ordered pairs (a, b) of positive integers for which the numbers**

**(a**

^{3}b – 1)/(a + 1) and (b^{3}a + 1)/(b – 1)

**are both positive integers.**

Both questions have solutions, and similar methods, but the real question has fewer of them. Feel free to try both. Also, note that 0 is not a positive integer.

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