Elementary Number Theory -1: Divisibility-1

This the first video of the series on ENT. I am not an expert in Number theory. The reason for the series is threefold: (i) A thorough conceptual understanding of ENT will serve you well when you learn Algebra. (ii) In the beginning, many of the results can be proved in a few sentences. Hence it is perfect training ground for students who want to improve their writing skills. (iii) One can also hone one's problem solving skills by attempting many problems.

But I have my own reservations about (iii). Many Number theory enthusiasts showcase their talent in solving Olympiad type problems rather than focusing on those which allow a beginner to cut his teeth into. I would confine myself to those problems within my reach!

The topics I plan to cover (in the series!) are:
(i) Divisibility
(ii) Division Algorithm
(iii) GCD, LCM, Bezout idenitity, Eulcid's algorithm
(iv) Linear Diaphontine equations
(v) Primes and the Fundamental Theorem of Arithmetic
(vi) Congruences
(vii) Chinese remainder theorem.
(viii) Divisibility tests (if I feel like)
(ix) Euler's totient function

Timestamp
0:00 Disclaimer
0:50 Aim,reasons and suggestion for this series
6:09 Divisibility definition
9:21 Uniqueness of such an integer
14:20 Suggestion to students
15:36 Question -1
16:33 Question -2
18:20 Question -3
20:45 Question -4
23:08 Question -5
25:00 Question -6
26:00 Question -7
29:08 Some interesting problems
38:48 Question -8
42:25 Question -9
48:38 Question -10
53:13 Suggestions
54:31 Outro

[sachinadhikari]

We just completed our course of Modern algebra in 4th sem without number theory in college as elementary number theory is in MSc 1st sem in our university and i know the pain of not knowing number theory but when I got a chance to learn number theory at MTTS LO this year, most of things in modern Algebra start making sense .

Now I can recommend my juniors these lectures before they jump on modern Algebra in next semester
Thank you professor 👏

[jidrit]

I found this subject hard. I didn't know how to start questions.

[ndmaphy]

Hi Sir,

Why don't you want to record series on Differential Geometry whether most of people's are waiting madly 😢

[rinkubharali]

Thank you Sir. Sir do you have plane to make a course on rigorous *multiple integral* otherwise it becomes (like you say) *circus* for us, calculate this, calculate that and what not, nothing clear what makes this things work.

[RohitYadav-rnnm]

sir please make video on differential geometry regarding as how to approach and what way to study differntial geometry

[ramjipathak]

Which book is a better to deep study for elimentary mathematics .

[anonymousmath]

Respected Sir, whether Galois theory you plan to record in near future?

[ashutoshkumar]

Sir, what is your plan after number theory ? Analysis (Measure Theory, functional analysis, ..) or Algebra?