# Tagged Questions

Modular arithmetic (clock arithmetic) is a system of integer arithmetic based on the congruence relation $a \equiv b \pmod{n}$ which means that $n$ divides $b-a$.

46 views

### Modular exponentiation

How do you solve: $$5^{{9}{^{13}}^{17}} \equiv x\pmod {11}$$ I've been trying with this but no luck. I get to ${{9}{^{13}}^{17}} \equiv x\pmod {11}$ from $5^3 * 5^3 * 5^3 = 64 \equiv 9\pmod {11}$. ...
65 views

### Quick methods to check perfect$4^{th}$,$5^{th}$, $6^{th}$ powers

Are there any quick modulus methods to check if a number could be a perfect power (4, 5, 6)? Preferably binary methods. For example, a perfect fourth power has to be $0, 1 \pmod{16}$ from a square ...
40 views

### Finding solutions to $h(j)=15+j^2 \mod 17, j \in \mathbb{N}$

I have a function such as this: $$h(j)=15+j^2 \mod 17, j \in \mathbb{N}$$ When $h(j)=7$ I know that there is a solution to this as: $h(3)=15+(3)^2 \mod{17}=7$ How can I prove that there no solutions ...
71 views

82 views

### When can I stop checking if $\varphi(n)$ is equal to some integer - Euler Totient Function

Take the example $\varphi(n) = 12$ After I split into factors $(12 \times 1), (6 \times 2), (4 \times 3)$ I know that $\varphi(13) = 12$ and $\varphi(2) = 1$, hence $n = 13 \times 2 = 26$ is ...
61 views

### Modulo operation property

If $x =(a+b) \pmod m$ and we know `$(a+b)\pmod n=(a \pmod n+b \pmod n) \pmod n$ Can we write: $b = (x-a \pmod m)%m$ Please correct me if I am wrong.
39 views

166 views

### I can't use Chinese Remainder Theorem.

I have a problem with: $$\begin{cases} 6x\equiv 2 \mod 8 \\ 5x \equiv 5 \mod 6 \end{cases}$$ I want to use the Chinese Remainder Theorem, but I can't because of the fact $\gcd(8,6) > 1$. How can ...
51 views

### System modular equation.

Consider: $$\begin{cases} x\equiv 2 \mod 4 \\ x \equiv 2 \mod 6 \end{cases}$$ And we would like use Chinese remainder theorem but we can't because $\gcd(4,6) > 1$ How can I deal with it.
359 views

### Encryption with large mods

I am studying for a cryptography final and I have come across something I can just not figure out. My math background is rather weak. This is related to RSA and concerns itself with raising numbers ...
59 views

### Modular equation with $x^2$

For $x \in \mathbb{Z}_{200}$solve this modular equation $$(x-1)(x-2) \equiv 0 \mod 200$$ I don't know how to deal with that $x$ occurs in second power, I mean $x^2$ I am asking for advice.
128 views

### How to continue solving? Perfect Cuboid

I am doing research on perfect cuboids, and I'm looking for values $a,b,c$ such that the following is integer, and I'm not sure how to continue this. Any suggestions are appreciated! $PED$ is a very ...
76 views