phi

See also: Euler Phi function

created by Xamot

(thing) by N-Wing (3.5 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 (1.9 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

Y'know, if you log in, you can write something here, or contact authors directly on the site. Create a New User if you don't already have an account.

Login
Password

remember me
password reminder
register

Everything2 Help

Drink up!
The Language of Flowers
Marvel Comics
An Argument Against the Abolishing of Christianity
In praise of older women
James Joyce
preserved lemons
X-Men
STS-107
space war
John Brown
Halley's Comet
The Satires of John Donne
Thomas Shadwell

cryforhelp
Major dictionaries of the world	(review)
Glowing Fish
The Uncanny X-Men and the New Teen Titans	(thing)
WolfKeeper
Launch loop	(idea)
TendoKing
Katana	(person)
Wuukiee
Highly ornamental cultivars of brambles still have as many thorns as their wild counterparts	(idea)
TheDeadGuy
Editor Log: May 2008	(log)
everyday j.Lo
pray do not molest them	(thing)
ammie
Bands Who Take Their Names from Eighteenth-century English Poetry and Prose	(idea)
shaogo
Under My Thumb	(review)
ammie
Rock On	(person)
The Custodian
The Dresden Files	(thing)
Ouzo
PETA becomes you, a proposed future	(fiction)
Ereneta
Stone Soup, Part Two	(fiction)
jjen
Sorrier than I ever thought I would be	(personal)
locke baron
Moskva class antisubmarine cruiser	(thing)

Everything 2 is brought to you by the letter C and The Everything Development Company