“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…

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