3
votes
1answer
46 views

Number theory notation

I am confused with the below notations . I know that ($a \equiv b \mod {n} )\iff ( n|(a-b)$ ) but what the below notation says ? $a = b \mod {n}$ and in theorem 16 in this ,it's given as below ...
1
vote
0answers
26 views

Mistake involving Chinese remainder theorem

I ran into a snag in attempting to solve the following problem. $$x\equiv r\pmod p$$ $$x\equiv0\pmod q$$ I did the following $$x=k_1q=k_2p+r$$ $$k_1q\equiv r\pmod p$$ $$k_1\equiv rq^{-1}\pmod p$$ ...
2
votes
0answers
69 views

Lucas Number Equivalent of the Pisano Period?

I'm doing some work with the Pisano Period, and it's leading to also talk about the Lucas numbers $mod \ m$, and their period. Is there a specific notation already designated? Sticking with using a ...
0
votes
1answer
25 views

General notation for indicating the last digit of a given power

Let's say I wanted to state, for example, what's the last digit of a power with a base of a number ending with 4 as its last digit. Casually, I'd just write it down as: $$...4^{2n}=...6 \\ ...
0
votes
0answers
38 views

Difference Between Equivalence and Congruence

Sometimes I read $a \cong b$ (mod $n$). At other times, I read $a \equiv b$ (mod $n$). What's the difference?
0
votes
2answers
91 views

difference between mod 7 and (mod 7)

So, I am studying modular division right now, and I want to clarify one thing. $a = b \mod m$ and $a = b \pmod m$ Is the top one $b = mk + a$ ($k$ is an integer) and the bottom one is $a = mk + ...
1
vote
2answers
134 views

Random math questions (modular arithmetic & notation)

I found this amazing wall clock picture on the internet but I really don't know a few things. I don't know what's $B'_L$, 3, why $2^{-1}\equiv 4[7]$ and ...
3
votes
1answer
76 views

Stumped by a notation.

I'm reading through http://cr.yp.to/papers/primesieves.pdf and came across the following notation on p. 1: For example, a squarefree positive integer $p \in 1 + 4\Bbb Z$ is prime if and only if ...
0
votes
2answers
88 views

Meaning of $\bar{i}:=i+n\mathbb{Z}$ in Modular Arithmetic

I am starting to learn graph theory and ran into the following definition: The set $\mathbb{Z}/n\mathbb{Z}$ of integers modulo $n$ is denoted by $\mathbb{Z}_n$; its elements are written as ...
2
votes
3answers
66 views

Convenient way to write $x \bmod{n}$

I'm trying to figure out an easy way to write $x \bmod{n}$. For example, in this exercise, where I need to show that this is an homomorphism: ...
3
votes
1answer
53 views

When does a solution to $a^x\equiv b\pmod m$ exist, and how is the smallest solution denoted?

Given fixed integers $a,b,m$ such that $\gcd(a,m)=1$, how do I know if there exists an integer $x$ such that $a^x\equiv b\text{ mod } m$, also if a solution does exist, what is the typical notation ...
0
votes
2answers
87 views

Inconsistent definitions of “quadratic residue” versus (linear) “residue”?

The Legendre symbol $(94 / 59)$ is equal to $1$, therefore, by definition, $94$ is a quadratic residue mod $59$. At the same time, the residue of $a\mod n$ is defined as the (positive) remainder when ...
1
vote
3answers
252 views

Modulus of inverse of a number

In the Chinese Remainder Thm., $y_i$ is the modular inverse of $\frac{P}{p_i}$, where $p_i$ is the $i$th modulus in a set of $n$ congruencies and $P$ is $\prod_{i=1}^np_i$ (right?). So if I calculated ...
1
vote
2answers
879 views

The right way to write modulus equation?

I came from computer forum, and I came across many different expression of modulus equation, which of the following is authentic ? ...
4
votes
3answers
254 views

Is it mathematically correct to write $a \mod n \equiv b$?

This is not a technical question, but a question on whether we can use a particular notation while doing modular arithmetic. We write $a \equiv b \mod n$, but is it right to write $a \mod n \equiv ...
1
vote
1answer
776 views

Notation for modulo: congruence relation vs operator

If a and b are congruent modulo a number c, we might write $a \equiv b \pmod c$. When writing programs, it's often useful to compute the remainder after division, and in pseudocode we might write a = ...
2
votes
5answers
198 views

Confused about modular notations

I am little confused about the notations used in two articles at wikipedia. According to the page on Fermat Primality test $ a^{p-1}\equiv 1 \pmod{m}$ means that when $a^{p-1}$ is divided by $m$, ...