Question

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

Answer 1

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

Answer 2

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

Answer 3

yes, so what must n be?

Answer 4

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

Answer 5

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...

\[1457\mod297 = 269,\text{ } 1754\mod297 = 269\]

Answer 6

sorry, n is as large as possible

Answer 7

Thanks!