AIME #7 1985

[stupidityismygam]

Assume that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are positive integers such that [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] Determine [unparseable or potentially dangerous latex formula]

[bradp]

well.. i tried some guess and check

obviously if a is x^4 then b must be x^5

if [unparseable or potentially dangerous latex formula] then c would be 35... and [unparseable or potentially dangerous latex formula] doesn't have a perfect square root

so... [unparseable or potentially dangerous latex formula] then c would be 100.
[unparseable or potentially dangerous latex formula]
d = 1000
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

[stupidityismygam]

no guess and check solution

[unparseable or potentially dangerous latex formula] so let [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula] so let [unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Since [unparseable or potentially dangerous latex formula] is prime [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula] (only positive [unparseable or potentially dangerous latex formula] since [unparseable or potentially dangerous latex formula] is positive)

So, then [unparseable or potentially dangerous latex formula]

[bradp]

aime is answer only !

[bradp]

oh.. i thought you were telling me i couldnt do guess and check. i guess i just assume everything you tell me is negative.

[mathpimp]

Are you guys just creating [unparseable or potentially dangerous latex formula] to solve the problem? Where'd it come from?

[bradp]

i created x to solve the problem.

i wont speak for the other mathematician in this thread

[stupidityismygam]

[mathpimp]

Okay yeah, that second one is how I started solving it. Then I looked and saw a solution had already been posted. So I was like m, n, wtf? You certainly made it look a lot cleaner, it would be a pain to Latex it up with all those radicals and junk.

[bradp]

guess and check suc-kers

[mathpimp]

Yeah, that works. But is it really the manly way to get it done? Just messin with you Brad. Yeah had I actually been alive and a high school student in 1985 that's probably how I would have done it but I find it more fun to work it out algebraically, since we aren't in a testing situation here.

[bradp]

don't attack my mathliness/manliness