# Math Help - consecutive positive

1. ## consecutive positive

Find a set of three consecutive positive integers such that the small-
est is a multiple of 5, the second is a multiple of 7 and the largest is amultiple
of 9.

2. Originally Posted by perash
Find a set of three consecutive positive integers such that the small-
est is a multiple of 5, the second is a multiple of 7 and the largest is amultiple
of 9.
$x \equiv 0 mod(5)$
$x + 1 \equiv 0 mod(7)$
$x + 2 \equiv 0 mod(9)$

Can you solve that system of congruences?

3. Originally Posted by colby2152
$x \equiv 0 mod(5)$
$x + 1 \equiv 0 mod(7)$
$x + 2 \equiv 0 mod(9)$

Can you solve that system of congruences?
Yes.
This is equivalent too.
$x\equiv 0(\bmod 5)$
$x\equiv 6(\bmod 7)$
$x\equiv 7(\bmod 9)$.

Using the Chinese remainder theorem (details ommited) all the numbers that satisfy this are: $315k+160$ where $k\in \mathbb{Z}$.

This is Mine 9th Post!!!