Category:Euler Phi Function
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This category contains results about the Euler $\phi$ function.
Definitions specific to this category can be found in Definitions/Euler Phi Function.
Let $n \in \Z_{>0}$, that is, a strictly positive integer.
The Euler $\phi$ (phi) function is the arithmetic function $\phi: \Z_{>0} \to \Z_{>0}$ defined as:
- $\map \phi n = $ the number of strictly positive integers less than or equal to $n$ which are prime to $n$
That is:
- $\map \phi n = \card {S_n}: S_n = \set {k: 1 \le k \le n, k \perp n}$
Subcategories
This category has the following 10 subcategories, out of 10 total.
E
I
Pages in category "Euler Phi Function"
The following 96 pages are in this category, out of 96 total.
4
C
- Cardinality of Reduced Residue System
- Consecutive Integers with Same Euler Phi Value
- Consecutive Triples with Same Euler Phi value
- Consecutive Triples with Same Euler Phi value/Examples
- Consecutive Triples with Same Euler Phi value/Examples/5186
- Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n
E
- Euler Phi Function by Argument is Injective
- Euler Phi Function in terms of Möbius Function
- Euler Phi Function is Even for Argument greater than 2
- Euler Phi Function is Multiplicative
- Euler Phi Function is not Completely Multiplicative
- Euler Phi Function of 104
- Euler Phi Function of 117
- Euler Phi Function of 135
- Euler Phi Function of 1364
- Euler Phi Function of 140
- Euler Phi Function of 148
- Euler Phi Function of 152
- Euler Phi Function of 164
- Euler Phi Function of 168
- Euler Phi Function of 2 times Odd Prime
- Euler Phi Function of 216
- Euler Phi Function of 228
- Euler Phi Function of 234
- Euler Phi Function of 248
- Euler Phi Function of 25,940
- Euler Phi Function of 252
- Euler Phi Function of 256
- Euler Phi Function of 264
- Euler Phi Function of 270
- Euler Phi Function of 315
- Euler Phi Function of 316
- Euler Phi Function of 33,817,088
- Euler Phi Function of 420
- Euler Phi Function of 5188
- Euler Phi Function of 52
- Euler Phi Function of 524
- Euler Phi Function of 525
- Euler Phi Function of 56
- Euler Phi Function of 60
- Euler Phi Function of 616
- Euler Phi Function of 630
- Euler Phi Function of 666 equals Product of Digits
- Euler Phi Function of 72
- Euler Phi Function of 735
- Euler Phi Function of 76,326
- Euler Phi Function of 76,332
- Euler Phi Function of 76,338
- Euler Phi Function of 76,344
- Euler Phi Function of 824
- Euler Phi Function of 825
- Euler Phi Function of 84
- Euler Phi Function of 90
- Euler Phi Function of 944
- Euler Phi Function of 945
- Euler Phi Function of 975
- Euler Phi Function of Integer
- Euler Phi Function of Integer/Corollary
- Euler Phi Function of n equal to Euler Phi Function of n+3
- Euler Phi Function of Non-Square Semiprime
- Euler Phi Function of Power of 2
- Euler Phi Function of Prime
- Euler Phi Function of Prime Power
- Euler Phi Function of Prime Power/Corollary
- Euler Phi Function of Product
- Euler Phi Function of Product with Prime
- Euler Phi Function of Square-Free Integer
- Euler Phi Function preserves Divisibility
- Euler Phi Function/Examples/Phi is 6
- Euler Phi Function/Table
I
L
N
- Number of Non-Dividing Primes Less than n is Less than Euler Phi Function of n
- Numbers for which Euler Phi Function equals Product of Digits
- Numbers for which Euler Phi Function of 2n + 1 is less than that of 2n
- Numbers n whose Euler Phi value Divides n + 1
- Numbers such that Divisor Count divides Phi divides Divisor Sum
- Numbers with Euler Phi Value of 72
P
S
- Schatunowsky's Theorem
- Sequences of 3 Consecutive Integers with Rising Phi
- Sequences of Three Consecutive Strictly Increasing Euler Phi Values
- Smallest Even Integer whose Euler Phi Value is not the Euler Phi Value of an Odd Integer
- Successive Solutions of Phi of n equals Phi of n + 2
- Sum of Euler Phi Function over Divisors