Page 1 of 1
AIME #6 1983
Posted:
Sun Jul 01, 2007 2:43 pmby 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]
Re: AIME #6 1983
Posted:
Sun Jul 01, 2007 4:47 pmby Kurt
Posted:
Sun Jul 01, 2007 7:16 pmby 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.
Posted:
Sun Jul 01, 2007 8:39 pmby 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]