Trollathon 4-7

Level pending

a x − b y = 1 a^x - b^y = 1

How many integer solutions ( a , b , x , y ) (a, b, x, y) are there?

∞ \infty 0 1 Finitely many solutions but more than 1

Zi Song Yeoh by Zi Song Yeoh , 20, Malaysia

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1 solution

Zi Song Yeoh
Apr 28, 2014

Note that a = 1 , b = 0 a = 1, b = 0 and any positive integers x , y x, y will give us infinitely many integer solutions.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Gosh dang these problems. When they put you under "Hard Math", this is not what I was expecting at all. :O

Finn Hulse - 7 years, 1 month ago

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But note that this problem is similar to the Catalan's Conjecture, which has exactly one solution.

Zi Song Yeoh - 7 years ago

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Oh that is interesting. But seriously how are you under "Hard Math" when you have only one Level 4 4 problem? And @Daniel Liu has like 29 29 and I have 12 12 . Kind of strange, don't you think?

Finn Hulse - 7 years ago

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