How many integer value of x and y are there such that

4x + 7y = 3 where IxI < 500 and IyI < 500?

Any help would be appreciated.

Thanks,

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- August 13th 2009, 10:12 PMa69356Number of Interger value of x and y.
How many integer value of x and y are there such that

4x + 7y = 3 where IxI < 500 and IyI < 500?

Any help would be appreciated.

Thanks, - August 13th 2009, 10:28 PMGamma
All you need to do is find one solution, and you have all of them for this. Let be a solution to .

Then all other solutions will be of the form:

Where k runs through the integers positive and negative.

So in this case, inspections shows (-1,1) is a solution, so the others are :

I trust that you can take it from here