# Questions tagged [number-theory]

For questions related to the teaching of number theory, the part of mathematics concerned with properties of the positive integers.

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### Resources to introduce Modular arithmetic

We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
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### Limitations of applying the factor theorem

Here are three situations in which students might try to apply the factor theorem. Proving that $x + 1$ is a factor of the polynomial $x^3 + x + 2$ can be done using the factor theorem by showing ...
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1 vote
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### Whole numbers as sets vs abstracted properties of sets

I recently landed on a book written for elementary school teachers which introduced the concept of whole numbers in the following manner: We have a set $\{\alpha, \beta, \gamma\}$. There are other ...
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### congruency: how widely used?

Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used ...
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### What is the terminology for integers with the same oddness or evenness?

If two integers are either both negative or both positive, we can say they have the same sign. How about two integers that are either both odd or both even? Is there any term for them?
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### Reference request: an introduction to triangular, square, and other figurate numbers

There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that ...
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### Are there any mathematics based game apps which require students (between 10 - 16 years) to apply their maths knowledge to play the game

So, what we essentially mean is students will apply their knowledge on divisibility, factorization, prime numbers, lcm, gcf, decimals, fractions, etc to play the game. A somewhat different approach to ...
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Which academic subjects examine what the advantages and disadvantages of the various number bases are, e.g. besides base ten: base twelve, base sixteen, base eight, base two and the ways that they can ...
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### Why do we write numbers with decreasing place values?

This question came up while teaching ~16 year olds binary numbers. Why do place values increase to the left and not the other way round?
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1 vote
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### Number theory in an introductory course on discrete dynamical systems

Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
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### How can I explain construction of the Bézout's identity to my kid?

My kid is soon 7 years old, he could understand fractions, linear equation and modulo operation. I've just taught him Chinese remainder theorem, looking to introduce some more basic number theory ...
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### Introductory book or other resource on $p$-adic numbers/number theory/analysis

I am having problems understanding $p$-adic numbers/$p$-adic number theory/$p$-adic analysis. I have tried some notes on the internet, but these notes were not helpful. Can anyone suggest a book, ...
557 views

### Geometrical interpretation of the identity $\operatorname{lcm}(a,b) \operatorname{gcf}(a,b) = ab$

Does anyone know a good geometrical representation of the fact that $\DeclareMathOperator{lcm}{lcm}\DeclareMathOperator{gcf}{gcf}\lcm(a,b) \gcf(a,b) = ab$? Because $\lcm$ and $\gcf$ are abstract ...
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### Is there a numerical base that is in any way “better” for simple mathematical calculations than others?

I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level. I know that different numerical bases (i.e. decimal/...
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### What should I say about elementary number theory?

I need to give an option talk (a 10 min talk given to students who are selecting their options for sophomore mathematics) about an elementary number theory module. The students will have completed a ...
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### Analogy for multiplying modulo N

Sometimes I want to explain to laymen/new students/laywomen how addition modulo N works. There are some instructive analogies: Addition on the clock (12), Addition on weekdays (7). They illustrate the ...
648 views

### Could students learn a lot more from school if they're only taught number theory until way later?

According to https://www.inc.com/bill-murphy-jr/science-says-were-sending-our-kids-to-school-much-too-early-and-that-can-hurt-th.html, when students get taught a concept when they're so young, they're ...
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### How to arrive at infinitude of primes proof?

I know Euclid's proof of there being infinite number of primes. I want to let my brother (age 15) arrive at that proof by himself. He knows definition of a prime number (number divisible only by 1 and ...
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