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Find the least positive residue of $40^{128} \mod 49$

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#number-theory #elementary-number-theory #modular-arithmetic #totient-function
57
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An integer sequence defined from a variation of the Lucas–Lehmer primality test: the case of the Euler's totient function

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#elementary-number-theory #recurrence-relations #prime-factorization #totient-function
164
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On even integers $n\geq 2$ satisfying $\varphi(n+1)\leq\frac{\varphi(n)+\varphi(n+2)}{2}$, where $\varphi(m)$ is the Euler's totient

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#sequences-and-series #elementary-number-theory #prime-factorization #totient-function
51
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Is this identity satisfied by finite or infinite number of triples $(a,b,c)$ of natural numbers?

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#number-theory #totient-function
155
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The arithmetic function $\frac{\operatorname{rad}(2n)}{n+\varphi(n)+1}$ and a characterization of twin primes

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#elementary-number-theory #prime-numbers #prime-factorization #totient-function
101
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How to solve $\phi(n)=n$ for $n$?

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#elementary-number-theory #totient-function
231
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The Basel Problem, Cannonball Problem & 24-ness?

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#riemann-zeta #pi #totient-function #square-numbers #distribution-of-primes
310
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Find all postive integers $n$ such that $n+\tau{(n)}=2\varphi{(n)}$

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#number-theory #totient-function #conjectures #divisor-counting-function
214
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Find all postive integers $n$ such that $n+\varphi{(n)}=2\tau{(n)}$

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#number-theory #totient-function #divisor-counting-function
888
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A quick method to calculate $\phi(270)$ manually without the 'standard' formula

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#group-theory #inclusion-exclusion #totient-function
326
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Markov triples that survive Euler's totient function

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#elementary-number-theory #diophantine-equations #prime-factorization #totient-function
53
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On miscellaneous questions about perfect numbers I

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#elementary-number-theory #prime-numbers #totient-function #divisor-sum #prime-gaps
74
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On miscellaneous questions about perfect numbers II

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#sequences-and-series #elementary-number-theory #prime-factorization #totient-function #divisor-sum
158
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Summation question with Euler's totient function

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#elementary-number-theory #totient-function
298
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For which n is it true that $\phi(n^2)=\phi(n)+10$

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#number-theory #elementary-number-theory #totient-function

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