What is the largest positive integer n such that 1457 and 1754 leave the same remainder when divided by n?

Question

anonymous · Answer

$$1754=1457 \mod n \rightarrow \left( 1754-1457 \right)=0 \mod n$$

anonymous · Answer

1754-1457 = 297 so mod n => 297 = 0?

anonymous · Answer

yes, so what must n be?

anonymous · Answer

I'm just guessing but 297? Uhgg.. I don't know XD

anonymous · Answer

btw, they don't have a congreunce symbol so i had to use an = instead.

1457 = k*n + r,
1754 = c*n + r

where r is as large as possible. then if we subtract the two, we get
(1754 - 1457) = (c-k)*n + (r - r)
if we mod n each side, then we get the previous...

$$1457\mod297 = 269,\text{   } 1754\mod297 = 269$$

anonymous · Answer

sorry, n is as large as possible

anonymous · Answer

Thanks!