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.
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!!!