An awesome note by Masum bhai

[*Mahi*]

Here is an awesome note on number theory by Masum Bhai (Masum Billal) on number theory. It might help you on topics of Divisibility, Congruence and GCD,LCM with a discussion nice problem collection.

[nafistiham]

Thanks a lot, Masum Vai

[Sazid Akhter Turzo]

But the problems are very much easy.
Turzo

[nayel]

I was just looking at the note, and I wouldn't suggest taking this as your main text for learning number theory, as it contains a lot of wrong information. But once you have learned the basics from a proper book then there should be no problem in going through this.

[FahimFerdous]

@Nayel vaia: could you please give examples of some wrong informations? I haven't read it yet, but I will.

[nayel]

I personally don't think pointing fingers at someone's mistakes and sharing them in public without the notice of that person is a good thing to do, and I hope you'll never make me do it again. But because you asked, here are a few: there's no proper definition of quotient/remainder, nor a correct proof of their existence; section 1.2 contains a lot of wrong infos; improper definition of gcd and lcm (and of their existence) etc.

[FahimFerdous]

@Nayel vaia: I won't make you do it again. Thanks for this time.

[nayel]

@Mahi and Turzo: I am deleting both of your posts. This is not a place for quarreling.

[Masum]

I was just looking at the note, and I wouldn't suggest taking this as your main text for learning number theory,

I would like to suggest the same too.

as it contains a lot of wrong information. But once you have learned the basics from a proper book then there should be no problem in going through this.

Though I did it for my followers, I didn't check it again, and since I lost my tex file, it is incomplete. But I think it would be a help for the people if you share the mistakes(may be this will be boring to you).
Oh another confession I must do, as I said, it was for my friends. So I wrote it from a programming view, and since none of them were rigorous in proofs, I didn't really care for a proper formal definition(that certainly is not true for math olympians, as I understand). I just wanted them to have a good sense. But I am wondering about what was wrong in section $1.2$?

[Masum]

পোলাপান, তোমাদের আর যাই হোক $\gcd,lcm$ এইগুলার definition নিশ্চই শিখানের কোন দরকার নাই। যেইটা দরকার সেইটা হইল এইখানে যে প্রব্লেমগুলা আছে ওইগুলা সলভ করা।
বিগিনারদের জন্য কাজে আসতে পারে।