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From: William Elliot on 27 Jun 2010 03:11
On Sat, 26 Jun 2010, Deep wrote:

> Consider the following two equations for the given conditions.
>
> k^2 = [a^k + b^k ]/c^2 (1)
>
> k^2 = [d^k + (1/4)e^k]/f^2 (2)
>
> Conditions: a,b,c,d,e,f are all integers each > 1; k =5
> a,b,c are coprimes, b is even; d,e,f are coprimes,
> e is even.
>
By "a,b,c are coprimes" do you mean pairwise coprime or
collectively coprime?

> Conjecture: If (1) is impossible then (2) is also impossible.
>
some a,b in N\1, c in N with 25.a^2 = b^5 + 32.c^5
iff
some a,b in N\1, c in N with 100.a^2 = 4.b^5 + 32.c^5

> Any comment upon this conjecture will be appreciated.
>
Simplify and get rid of fractions.
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