(In reply to First little thought ...
by Steve Herman)
In fact, this can be proven.
if 5 (e.g.) is in the denominator of one of them (say b=5 wlog) then :
sum = (aefhi+5(dchi+gcef))/5cefhi
so for the sum to be 1
aefhi+5(dchi+gcef) = 5cefhi
i.e. aefhi is divisible by 5 which is not possible because 5 is relatively prime to all of those variables.
Similar reasoning can prove that 9 *6 and 9*3 cannot appear on the bottom of any fraction, nor can 8*2, 8*4, or 8*6.
Posted by Joel
on 2006-12-15 00:06:43