1. ## Equation in N2

Solve In :

2. Originally Posted by dhiab
Solve In :
If we rearrange the equation we find

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

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

For this to happen, $1000 - 19x$ needs to be a multiple of 13.

Have a go from here...

3. 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?)

4. Hello: Help .....Continu