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**RogueDemon** Yes, the statement must be true for all $\displaystyle x$and $\displaystyle y$ not $\displaystyle 0$, as the problem requests. But the problem mainly asks *for which numbers $\displaystyle a$* is the statement true. Of course, the statement is true if $\displaystyle -2 < a < 2$, but clearly the statement isn't $\displaystyle only$ true for those numbers. And, if I interpreted the question correctly (please correct me if I'm wrong), what is required is that I find *all* $\displaystyle a$ for which the statement is true. If I could just state a portion of that, I could easily say that the statement is true for one arbitrary number, such as $\displaystyle 1$, and that alone would qualify as a complete solution.

I'll be logging off now, but I'll be back later.

I've been trying to solve this problem for quite some time now. :/