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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