Math Is Fun Forum

Amartyanil

Member

From: Universe

Registered: 2013-05-27

Posts: 82

Number of integer solutions

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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"Every place is the center of the universe. And every moment is the most important moment. And everything is the meaning of life." ~ Dan Harmon

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Number of integer solutions

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!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Number of integer solutions

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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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob