# Fun with Simplifying Fractions

The number of integers $$x$$ with $$-2014 \le x \le 2014$$ for which the fraction $$\dfrac{x^2+2014}{x^2+2017}$$ is already in simplest form can be expressed as $$1000a+100b+10c+d$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are (not necessarily) distinct integers from $$0$$ to $$9$$, inclusive. Find the value of $$a+b+cd$$.

×