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lgs98jonee
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#1
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#1
Can any1 here please give me an example of a diophantine equation and how to solve it?
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JamesF
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#2
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A diophantine is an equation in more than 1 unknown, for which the solutions are integers.
9n + 17m = 9

For a method of solving this type of equation, look up Euclid's Algorithm.
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theone
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They're are loads of diophantine equations, jame's example is one of the more 'simpler' examples. Another one, far less obvious how to solve, is

3^y + 2^x = z^2, where x,y,z are positive integers. (This is an old BMO question).
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lgs98jonee
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#4
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(Original post by theone)
They're are loads of diophantine equations, jame's example is one of the more 'simpler' examples. Another one, far less obvious how to solve, is

3^y + 2^x = z^2, where x,y,z are positive integers. (This is an old BMO question).
a bit like q5 on this year's? so no trial and error then?
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makesomenoise
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#5
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Funny that because the mathematical riddle concerning Diophantus has only one unknown, the length of his life. Didn't know that term "Diophantine equations", nice useful snippet of knowledge there...
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elpaw
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#6
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you can use matrix methods for solving the simpler ones
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GH
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#7
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(Original post by elpaw)
you can use matrix methods for solving the simpler ones
Thats what one of my forend tried to do for the BMO ques and couldn't do it because it wasn't exactly the correct way. Or something similar
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theone
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#8
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(Original post by lgs98jonee)
a bit like q5 on this year's? so no trial and error then?
No to both questions
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