Hi - I've come unstuck on a problem as I've not seen the like before:

$\displaystyle x\equiv 1\mod\17$

$\displaystyle x\equiv 8\mod\15$

$\displaystyle x\equiv 3\mod\35$

With out going into too much detail regarding the finer details of solving this I proceeed as moduli are all co-prime as required ( I thought that if this was the case then it is definately solveable!?). However, when looking at the last equation I'm trying to solve:

$\displaystyle 10y\equiv 1\mod\35$

Here 10 and 35 are not co-prime so I cannot have an inverse or therefore solve it. If I rearrange the original equations to redefine $\displaystyle x\equiv 3\mod\35$ I end up with contradictions in the question.

How do I proceed? As mentioned, my understading is if the moduli are co-prime then an answer will always exist.

Your help would be greatly received.

BR, Felix