# Tagged Questions

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### 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 ...
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### 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 $$x=k_1q=k_2p+r$$ $$k_1q\equiv r\pmod p$$ $$k_1\equiv rq^{-1}\pmod p$$ ...
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### 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 ...
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### 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 \\ ...
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### 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?
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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 $a = mk + ... 2answers 136 views ### Random math questions (modular arithmetic & notation) I found this amazing wall clock picture on the internet but I really don't know a few things. I don't know what's$B'_L$, &#x33;, why$2^{-1}\equiv 4[7]$and ... 1answer 77 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 ... 2answers 91 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 ... 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: ... 1answer 54 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 ... 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 ... 3answers 260 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 ... 2answers 922 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 ? ... 3answers 255 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 ...
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 = ...
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 $m$, ...