# Tagged Questions

Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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### Totient Function $\varphi{(x)}=24$

I'm trying to solve for all $x$. I'm thinking I'd like to take advantage of the fact that $\varphi$ is multiplicative if the factors of a number are coprime. So let $x=ab, (a,b)=1$. This is not the ...
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### find the remainder when $19^{22}$ is divided by $92$.

find the remainder when $19^{22}$ is divided by $92$. Will Euler's totient function help us?
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### Distribution of integer solution pairs (x,y) for $2x^2 = y^2 + y$

I am looking for integer pairs $(x,y)$ that respect $$2x^2 = y^2 + y$$ For example $(6,8)$ is a solution for that. Simple solution is to enumerate on $x$ or $y$ and test if the corresponding ...
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### Dirichlet convolution for dummies

Can someone explain me meaning and usefulness of Dirichlet convolution? I know the concepts of summation function over divisors of number and its Moebius inversion. But how does it relate to Dirichlet ...
### Prove that $\gcd(n,p-1)=1$ if $p$ is the smallest prime divisor of $n$
Let $n$ be a natural number greater than $1$, and $p$ be the smallest prime divisor of $n$. How can I prove that $\gcd(n,p-1)=1$?