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**Amartyanil****Member**- From: Universe
- Registered: 2013-05-27
- Posts: 81

hi;

Of the equation \(3x + 2y = 18\), how many positive integer solutions are there?

Is there any elegant solution to this problem rather than just brute force?

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Hi Amartyanil,

Yes: try looking at that equation modulo 2 and modulo 3. From there you can deduce that *x* is a multiple of 2 and that *y* is a multiple of 3, which allows you to reduce that equation into something much simpler!

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,541

hi Amartyanil

If you have some centimetre squared paper then you could try plotting the straight line. The answer will be easy to spot then and you'll see a pattern

Bob

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