A General Proof of “The Theorem Wu”

Math Online Tom Circle

“The Theorem Wu” as submitted by Mr. William Wu on the public Math Research Papers site viXra (dated 19-Nov-2014) can be further generalized as follows :

The Theorem Wu (General Case)
Prove that: if p is prime and p> 2 , for any integer $latex k geq 1$

$latex boxed {(p – 1)^{p^k} equiv -1 mod {p^k}} &fg=aa0000&s=3
$

[Special case: For p=2, k = 1 (only)]

General case :
$latex p = p_1.p_2… p_j… $ for all pj satisfying the theorem.

Examples:
$latex p = 3, k=2, 3^2 = 9$
$latex (3-1)^9 = 512 equiv -1 mod 3^2 $
p = 9 = 3×3
p = 21= 3×7
p = 27 = 3×9 = 3x3x3
p =105 = 3x5x7
p =189 = 3x7x3x3

[Mr. William Wu proved the non-general case by using the Binomial Theorem and Legendre’s Theorem]

I envisage below to prove for all cases
by using…

View original post 294 more words

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About tomcircle

Math amateur
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