Assuming n is an integer (why else would you ask for it?) we can narrow it down rather quickly.
A simple upper bound is 133*4^(1/5) < 133*1.5 < 200
(I could probably do better but this is fine.)
Now to check factors.
I'll spare the details but using modular arithmetic one can easily show 2, 4, 8, 16 are factors but not 32.
3 and 9 are both factors but not 27.
There's only one number in the interval that is a factor of both 16 and 9: 16*9 = 144.
I'll admit I then used a calculator to prove this works (though it's not hard to do by hand, just tedious). Both sides equal 61917364224
. So the assumption n is an integer was correct.
Edited on January 7, 2013, 12:53 pm
Posted by Jer
on 2013-01-06 19:04:30