Beal conjecture - 4

Beal conjecture-4

In the three members like or unlike power relations both the Fermat’s assertion and Beal conjecture have some similarities and differences.

Similarities

1. All the members can be even, then the relation will be reducible.. All the member cannot be odd due to non-conservation of oddness.

2. One or two members but not all the three may be square or higher power but all the members cannot be square or with the same higher power.

3. FLT and Beal conjecture are mathematically true with fractional and rational or complex numbers.

4 . In irreducible form, FLT  and the Beal conjecture do not have a common prime factor among the members.   

Differences

1.According to FLT in ax  + by  = cz , a,b,c the base numbers cannot be positive integers when the exponents x,y,z are same and greater than 2.

 (an – 1)n  + (an  - 1)n+1   = [a(an  - 1)]n , where a and n are any two independent variables which gives a set of multi-power relations obeying Beal conjecture with exponents  (n,n+1,n).

[a(an + bn)]n  + [b(an  + bn)]n    = (an + bn) n+1  gives a set of multi-power relations with exponents (n,n,n+1)

[2n an+1]n+2  +  [2n an+1]n+2   = [2n+1 a n+2] n+1  gives  a set of such relatins with exponents  (n+1,n+1,n)