extended Generalized Mersenne numbers xGM(a,b,n)=(a^n-b^n)/(a-b)

extended Generalized Fermat numbers xGF(a,b,m) = a^2^m + b^2^m


2^2^(m+1)-1 = (2^1+1)(2^2+1)(2^4+1)(2^8+1)...(2^2^m+1)

F(m+1)-2 = F(0)F(1)F(2)F(3)...F(m)

a^2-b^2 = (a-b)(a^1+b^1)
a^4-b^4 = (a^2-b^2)(a^2+b^2) = (a-b)(a^1+b^1)(a^2+b^2)
a^8-b^8 = (a^4-b^4)(a^4+b^4) = (a-b)(a^1+b^1)(a^2+b^2)(a^4+b^4)
            ....
a^2^(m+1)-b^2^(m+1) = (a-b)(a^1+b^1)(a^2+b^2)(a^4+b^4)...(a^2^m+b^2^m)
    xGM(m+1) = xGF(0)xGF(1)xGF(2)...xGF(m)
xGF(m+1)-2b^2 = xGF(0)xGF(1)xGF(2)...xGF(m)