Theories (Day 1)

[sourav das]

Topics:

i)Divisibility;
ii)Division Algorithm;
iii)Primes;
iv)The Fundamental Theorem Of Arithmatic
v)G.C.D.

You can follow Barton's Nomber theory book: (Sections: 2.1 , 2.2, 2.3, 3.1)
And also can study from 104 Number theory problems (First 5 topics)

Study hard, try to understand all by yourself first. If you really get stuck somewhere, Post the topic and problem in understanding that. Give a link to that thread here.

(Day 2 will start tomorrow 4:00 P.M.)

[sourav das]

No question still now ? Is there any beginner participating this camp???

[itsnafi]

BOMC-2 is my 1st online camp.so,am I a beginner?

[sourav das]

Actually the beginners are those who are new at problem solving and interested to learn first then problem solving...

[sowmitra]

Well, Vaia, here's a beginner for you.
Problem: If $d=(a,b)$, then, could we PROVE that there exists integers $s$ and $t$ such that $sa-tb=d$ ? (This is a problem from Adler's Book. Although I know that this is true, I have not been able to prove it )

[sm.joty]

No question still now ? Is there any beginner participating this camp???

I'm not only beginner but also "Moha beginner"
Now please explain me this.
http://www.matholympiad.org.bd/forum/vi ... 9917#p9917

[sm.joty]

Well, Vaia, here's a beginner for you.
Problem: If $d=(a,b)$, then, could we PROVE that there exists integers $s$ and $t$ such that $sa-tb=d$ ? (This is a problem from Adler's Book. Although I know that this is true, I have not been able to prove it )

Well, at first assume $m=sa-tb$ then use Euclidean Algorithm to write $a=qm+r$ then try to prove that $d=m$.

If this hint is not enough then see this but I discourage you to see this.

Theorem 1.5 of the book,"The Theory of Numbers" by "Adler"

[sowmitra]

Vaia, sorry, I made a mistake.
The actual problem wrote :$s$ and $t$ have to be positive integers.
I read Theorem-1.5. But, in it $s$ and $t$ may be positive or negative integers.