Some suggestions (BOMC-2)

[sourav das]

Actually I'm a little bit confused , today (now it is yesterday) is the first day of the camp but i didn't see much response from you. I think everyone is expecting some guide lines. I'm suggesting a few:

Level:1

i)Basic divisibility;
ii)Euclidean algorithm;
iii)properties of $g.c.d$ and $l.c.m$
iv)Concept of congruence

Level:2

Clear your concepts and learn useful properties about
i)Prime
ii)Co-prime
iii)Number of co-primes
iv)Number of divisors
v)sum of divisors

Level:3

i)Bezout's identity
ii)Solutions of $ax+by=1$
iii)Multiplicative inverse $ax\equiv 1$ $(mod$ $n$) $(a,n)=1$
iv)Fermat's little theorem;
v)Euler's toient function and Euler's theorem;
vi)Wilson's theorem

Level:4

i)Order,primitive roots
ii)Quadric residue
iii)Diophantine equations (begainning)
iv)Chinese Remainder theorem

Level: (*) [I'm still learning these things and use of these]

i)Pell's equation
ii)Lifting the exponent
iii)Zsigmondi's theorem
iv)Deep study with Diophantine equations
v)Bertrand’s Postulate
vi)Wolstenholms theorem

Level (combination study)

i)Vieta jumping with infinite discent
ii)Using tricks of congruence in Diophantine equations (having squares and cubes)

I think I've skipped a lot but when you'll study them, you'll understand what you'll need to learn other than these.
As, difficulty level is relative, anyone can start from his or her suitable level or any suitable topic.

For any problem in understanding something, just post in forum in a new thread and give a link here. But my request will be, first try to understand it all by yourself and don't give up before giving up....

[Sazid Akhter Turzo]

এত hidden করার কী আছে ? সরাসরি বললেই হয় ।
Turzo

[Tahmid Hasan]

Here's another interesting theorem:Lagrange's theorem
ohkawa.cc.it-hiroshima.ac.jp/AoPS.pdf/lagrange0.pdf