What's the least positive integer,
n, having the following properties:
 n = (a^2)/2
 n = (b^3)/3
 n = (c^5)/5
(where a, b, and c are integers)
Well, n=0 works but it's not positive (unless zero positive is "the least positive")
Otherwise, a must be a power of 2; b a power of 3; c a power of 5
((3*c^5)/5)^(1/3) = b
((2*c^5)/5)^(1/2) = a
Need to find a value for c such that both of the above equations yield integers.
I'm not sure how much this helps, probably not very much, but here are some values where 2 of the 3 original conditions are true (ie 1 of the 2 above equations):
a=12 b=6 n=72
a=96 b=24 n=4608
a=324 b=54 n=52488
a=200 c=10 n=20000
a=6400 c=40 n=20480000
b=1125 c=75 n=474609375
a=48600 c=90 n=1180980000
Edited on November 27, 2004, 5:07 pm
Edited on November 27, 2004, 5:08 pm

Posted by Larry
on 20041127 16:59:21 