# Let n be a-positive integer

1. Jan 23, 2008

### Gnoj

let n be a-positive integer. Prove that a and c leave the same remainder if and only if a - c =nk for some integer k.

2. Jan 24, 2008

### Himanshu

Suppose that

$$\normalsize A=nQ_{1}+R_{1}$$

and

$$\normalsize C=nQ_{2}+R_{2}$$

substract the two equation to get

$$\normalsize A-C=n(Q_{1}-Q_{2})+(R_{1}-R_{2})$$

but the equation

$$\normalsize A-C=n(Q_{1}-Q_{2})$$

requires that

$$\normalsize R_{1}=R_{2}$$

Therefore the above result.

Last edited: Jan 24, 2008
3. Jan 24, 2008

Thank You