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malaygoel · #3 July 3rd, 2009, 03:06 AM

Quote:

Originally Posted by Prove It

$y = \frac{1000 - 19x}{13}$ .

You need to substitute an integer $x$ in order to get an integer $y$ .

$y = \frac{1001-1 - 13x-6x}{13}$

$y = 77-x-\frac{1+ 6x}{13}$ .

The smallest value of x that will satisfy is 2. Since gcd(6,13)=1, the next next value will be 2+13=15, the next 28 and so on.

The largest value of x is less than or equal to $[\frac{1000}{19}]$ (Why?)