phi is a letter in the Greek alphabet.

The upper case form, Φ , means:

The lower case form, φ , means:

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.
The prime power decomposition of 100 is:
phi(100) is therefore:
= 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.

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