# Tag Info

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### How to read m $\bot$ n in totient function?

The only meaning that makes sense is that $m\bot n\iff \gcd(m.n) = 1$. Though I must admit that I never saw this notation before, and without the context I wouldn't have guessed what it's supposed to ...
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### Show that there are infinitely many positive integers $n$ for which $\phi(n)^2 + n^2$ is a perfect square.

Let $n=3^k\cdot 5$ for $k\ge 1$. Then we have $\phi(n)=8\cdot 3^{k-1}$, and hence $$n^2+\phi(n)^2=3^{2k}\cdot 5^2+8^2\cdot 3^{2k-2}=(3^{k-1})^2(9\cdot 5^2+8^2)=(17\cdot 3^{k-1})^2.$$ This holds for ...

### What are phi and tau defined as?

$\phi(n)$, known as Euler's totient function or phi function given the number of positive integers not exceeding $n$ and relatively prime to $n$. For example, $\phi(6)=2$ because $1$ and $5$ are the ...
1 vote
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### Why need of totient function to find generators of cyclic group $C_n$?

First, I am your downvoter. You keep biting off more than you can chew. It's quite a mess. However, here's one more college try: A basic fact about cyclic groups, which it would be great progress ...
1 vote
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1 vote
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### Is there a combinatorial proof that Euler's totient function divides Jordan's totient function?

Equivalently, $J_k(n)$ counts the $k$-tuples $(a_1,\cdots,a_k)$ of elements of $\mathbb{Z}/n\mathbb{Z}$ which generate the whole ring (as an ideal). We can verify $(\mathbb{Z}/n\mathbb{Z})^\times$ ...

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