guys... It's high time that I get an answer... atleast say that you're working on it..
let , c = b^2
now, finde natural numbers a and b which satisfies
a^c = b^a
This is what i did, I factoried a and b in terms of their HCF and a coprime number to g4t
a = n*p
Then after substituting in te above equation I got an expression, then I took 2 cases, where either the exponents of a and b are equal OR exponent of a > b's
either b^2 = a
or b^2 > a
==> b^2 = a*n
==> b is the GM of a and n ( for any n element N and a also element N )
so one pair of soluton is a = b = 1 ..
I cant get teh others guesssing seems like abad idea even after getting b = (an)^1/2
please help, thnks!