phi

See also: Euler Phi function

created by Xamot

(thing) by N-Wing (2 d) (print) ? (I like it!) Thu Dec 16 1999 at 7:55:49

phi is a letter in the Greek alphabet.

The upper case form, Φ , means:

Φ angle function

The lower case form, φ , means:

φ angle (mathematics)
φ Golden Ratio (mathematics)

(idea) by Kyberneticist (2 y) (print) ? (I like it!) Mon Dec 18 2000 at 22:45:45

In number theory, a number used to satisfy the following congruency.
a^phi(b) mod b = a
Where a and b are arbitrary integers.
Phi is calculated by generating the prime power decomposition of b, then applying the algorithm p^n = p^n-1*p-1 for each base in b.
Example:
The prime power decomposition of 100 is:
2^2*5^2
phi(100) is therefore:
2^(2-1)*(2-1)*5^(2-1)*(5-1)
= 2*5*4
= 40

Developed by Euler as a generalization of Fermat's little theorem, a^phi(b) mod b is very useful in public key cryptography.

printable version
chaos

Golden ratio	Euler Phi function	Ø	phi phenomenon
Prime decomposition	Why 'ph' and not 'f'?	φ	1/x = x-1
There's a reason that a funeral is not a celebration	Mathematics of RSA	Phi Kappa Theta	The real reason pi was never calculated to a high precision in ancient times
Greek alphabet	Euler	e	mathematics
public key cryptography	LSD	PSI	silver mean
Marc Favreau	angle	theta	Euler's theorem

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