AIME #6 1983

[stupidityismygam]

Let [unparseable or potentially dangerous latex formula] equal [unparseable or potentially dangerous latex formula] Determine the remainder upon dividing [unparseable or potentially dangerous latex formula] by [unparseable or potentially dangerous latex formula]

[Kurt]

[mathpimp]

I was just about to say that! Good job Kurt, with the whole "mod" language and all that. I'd have to explain it in my retard terms, but I got the logic at least.

[stupidityismygam]

yep yep yep...i'll post my alternate solution

Notice that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] so

[unparseable or potentially dangerous latex formula] then by the binomial theorem we see that [unparseable or potentially dangerous latex formula]

Also, [unparseable or potentially dangerous latex formula]

By adding these we see that every other term cancels, which simplifies to [unparseable or potentially dangerous latex formula]

Taking this [unparseable or potentially dangerous latex formula] gives [unparseable or potentially dangerous latex formula]

Quick division shows that the remainder is [unparseable or potentially dangerous latex formula]