Discovery #297
Conjecture (Papava). If gcd(a,b)=1 and a+b=c then
c<rad(abc)log[rad(a), a]log[rad(b), b]log[rad(c), c].
Result 1. Fermat's Last Theorem.
An equation x^n+y^n=z^n, n>2 has not a solution.
Proof:
z^n<xyz log₂x^n log₂y^n log₂z^n<z³n³(log₂z)³<z³z³z³=z⁹
n<9.
Result 2. Beal conjecture (Prize $1000 000).
...
|