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.
$\displaystyle x \equiv 0 mod(5)$
$\displaystyle x + 1 \equiv 0 mod(7)$
$\displaystyle x + 2 \equiv 0 mod(9)$

Can you solve that system of congruences?

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

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

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

This is Mine 9th Post!!!