Diophantine Pairs

Once upon a time, there was a chap called Diophantus (250 A.D.), who was interested in the problem of solving equations which had a whole range of possible answers.

It sounds as if this would make the Problem easier, not harder, but the real Problem wasn’t finding an answer, but deciding how many answers there were altogether.

We now use his name to describe any equations whose (multiple) solutions have to be Integers

The Problem: 

Solve these Diophantine equations, where x and y must be positive Integers.

 1.                              (Not many answers…)

 2.                              (Lots of answers e.g. x = 48, y = 9 - find as many as you can)

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Last modified: June 18, 2007