=> n<3 [abc<>0]
=> n<3 [abc<>0]
Proof:
Basis for induction always exists (for any p):
[mod 4]
Choose any even a, odd b, 
.
Inductive hypothesis:
[mod 
] (1)
=> there exists 
s.t. 
[mod 
] (2)
=> 
[mod 
] [By Wanless' Theorem] [
from (1)]
=> 
[mod 
] [By Wanless' Theorem]
=> 
[mod 
] [By Wanless' Lemma from (2)] [i>1]
By mathematical induction:
[mod 
] [m>1] with: 
[mod 
]
So:
[mod 
] [m>1] with: 
[mod 
]
Let m -> 99999…:
with: 
[if p>2]
So, there is no smallest 
, and therefore, by Fermat's Method of Infinite Descent, no non-zero A, B, C.
But, no pth power [p>2] (together with Fermat's work for n=4) => no nth power [n>2].
Copyright 1997 James Wanless