# 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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### How to explain what is wrong in this "proof" that $\sqrt N$ must be irrational?

Here is the problem that I asked undergraduate students of an introductory number theory course to prove: Prove that if $N$ is a nonsquare natural number, then $\sqrt N$ is irrational. Many ...
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### "Seeing" GCD and LCM in Word Problems

Last year, I taught GCD and LCM and then gave my students word problem relating to these concepts ("Two runners with given different speeds; when will they meet again?", "Having three kinds of flowers ...
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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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### How do i deal with students who make these mistakes? [closed]

I came across some interesting mistakes in many area of mathematics with my students and do not let me also to tell you for university students level, I would like to know How do i deal with ...
842 views

### 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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### 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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1 vote
187 views

### 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 ...
1 vote
185 views

### 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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1 vote
128 views

### Subject advice in Number Theory [closed]

At my University, we have the optional feature to write a project like a Bachelor Thesis. This semester have finished and I would like to work in the summer in project like this. So, I'm searching for ...
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1 vote
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### Does studying elementary number theory improve one's proof skills and ability to understand algebra and analysis? [closed]

I'm taking a number theory course and don't know whether it's worth it. I currently can't understand algebra and real analysis and decided to take # theory to see whether this would help me prove and ...
1 vote
160 views

### Interesting math lesson on integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs

I have to deliver a lecture for secondary school, about one of these topics: integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs. It should ...
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1 vote
131 views

### Pythagorean triples

What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is ...
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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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### When two equivalent algebraic statements have two "different" meanings

Suppose I want to prove $\sqrt{7}$ is not a rational number. I suppose it is and it brings me to a contradiction. Here how it goes line be line: First line. $\sqrt{7}=\frac{m}{n}$ Second line (...
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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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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 ...
94 views

### 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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