AIME #8 1983

[stupidityismygam]

if you post, you must post a solution...no cheating

What is the largest 2-digit prime factor of the integer [unparseable or potentially dangerous latex formula]

[zefuri]

61...i think becuase its greatest prime less than 200/3

[stupidityismygam]

correct, gj jeffrey

however, you should have brute # it

[zefuri]

THIS WAS A NUMBER 8?...basically you know if its two digit than 2 of the factors will be eliminated because of [unparseable or potentially dangerous latex formula]. So it must show up 3 times...which would be [unparseable or potentially dangerous latex formula] which is [unparseable or potentially dangerous latex formula]

[stupidityismygam]

1980 aimes were really easy
1990 aimes were hard
2000 aimes are medium

[bradp]

my solutions are better than these skimpy solutions

[stupidityismygam]

then post post away, the more solutions the better

[zefuri]

well usamos tomorrow so im trying to work as little as possible.

[bradp]

have fun

[stupidityismygam]

he is trying to work as little as possible tomorrow too

[bradp]

perhaps you could explain it then stephen

[zefuri]

okay well considering stephen died i will come out of my shall

Basically, if a factor occurs [unparseable or potentially dangerous latex formula] times in [unparseable or potentially dangerous latex formula]. It must occur [unparseable or potentially dangerous latex formula] times.

If the factor is [unparseable or potentially dangerous latex formula] then it will occur 4 times in the denominator if greater than 50 it will occur twice.

Since we need it to be the greatest we know that it must occur in the denominator twice. Thus, it must occur in the numerator [unparseable or potentially dangerous latex formula] times.

Hence, [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula].

So the greatest prime less than that would be [unparseable or potentially dangerous latex formula]