January 15, 2002
Practical Aspects of Modern Cryptography
Proof of Fermat’s Little Theorem
•
Inductive Step
•
•
Assume that
x
p
mod
p
=
x
mod
p
.
•
Then
(
x
+ 1)
p
mod
p
= (
x
p
+ 1
p
) mod
p
•
= (
x
+ 1) mod
p
.
•
Hence,
x
p
mod
p
=
x
mod
p
for integers
x
≥ 0
.
•
•
Also true for negative
x
, since
(-
x
)
p
= (-1)
p
x
p
.
