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$2n = \phi(a) + \phi(b)$

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#number-theory #totient-function #goldbachs-conjecture
118
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Find smallest $a \geq 0 \ s.t. \ a \equiv 11^{100} \ (mod \ 15)$

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#discrete-mathematics #modular-arithmetic #totient-function
298
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Prove that there are infinitely many integers $n$ such that $3\nmid\phi(n)$

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#number-theory #elementary-number-theory #divisibility #totient-function
276
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Is the equation $x = \phi(n), x=2k, n,k \in \mathbb{Z}$, where $\phi(n)$ is the Euler totient function, solvable for all evens?

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#divisibility #totient-function
317
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On $\phi(n) \sigma(n)$ being a square.

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#number-theory #analytic-number-theory #totient-function #divisor-sum
42
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Find all number $n\in \mathbb N$ such that $\varphi (n)=8$

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#totient-function
98
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How to calculate Euler Totients Function for a large number?

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#group-theory #totient-function
1.8k
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Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.

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#prime-numbers #totient-function #fermat-numbers
361
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Find the smallest positive odd integer n such that φ(n)/n = 7680/12121

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#elementary-number-theory #totient-function
144
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Number Theory Euler totient function

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#number-theory #totient-function
745
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Fast sieve for sum of Euler totient values (phi) values from 1 to 'n'

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#number-theory #algorithms #totient-function #sieve-theory
428
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Prove $(a,mn)=1\Rightarrow a^{{\rm lcm}(\phi(m), \phi(n))} \equiv 1 \pmod{\!mn} $

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#elementary-number-theory #solution-verification #totient-function
70
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There a infinity numbers of $n$ such that $ \phi (n) \equiv 0 \pmod{100} $

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#elementary-number-theory #totient-function
1.8k
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What is the remainder of $3^{13} \div 25$ by hand using Euler's theorem?

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#modular-arithmetic #totient-function
84
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Solving modular exponentiation

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#number-theory #modular-arithmetic #exponentiation #totient-function

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