shakil.ahamed's blog

Number theory practice problems.
By shakil.ahamed, history, 8 years ago, In English

Nothing is well understood unless we can apply it to solve some problems. Currently, I am learning number theory and there is no good classified list of problems for number theory. So, It is difficult to find some problem based on a specific topic.

Here I will maintain a list of problems of number theory in a few category. So, In near future, nobody have to face the same problem. Contribute interesting problems, people(mostly me :D ) will be grateful to you.

1. Divisibility/Primes/Co-prime/GCD/LCM
Problems:
1. LOJ: 1014, 1035
2. CF: 230B, 711E, 585E, 585C, 222C, 546D, GYM101212B
3. SPOJ: LCMSUMH
4. E-OLYMP: 1146, 1243, 1147, 1229, 1244, 1230

2. Continued Fraction
Problems:
1. UVA: 834
2. HackerRank: euler064

3. Diophantine Equations
Problems:
1. LOJ: 1077
2. CF: 7C

4. Functions: Counting Divisors/Divisor Sum
Problems:
1. LOJ: 1054
2. UVA: 13083

5. Function: Totient and Similar
Problems:
1. LOJ: 1007
2. SPOJ: NFACTOR , NDIV

6. Modular Arithmetic/CRT
Problems:
1. LOJ: 1067
2. CF: 687B, GYM100825A

7. Discrete Logarithms
Problems:
1. LOJ: 1325

8. Number Systems
Problems:
1. LOJ: 1028
2. E-OLYMP: 1001, 1002, 1008, 1013

9. Primitive Root
Problems:
1. E-OLYMP: 647

NB: This list is just created. And hopefully will grow with user contribution and as I learn. Thanks for being a part of it. :)

Contributors:
HaabyHings, Rudy1444, Lucas97, Batman, t3rminated, MladenP, TooNewbie

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8 years ago, # |
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Since you are already at UVA, you would make use of UHunt. UHunt classifies UVA problems according to topic, and it is accessed right through the menu of the page.

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    8 years ago, # ^ |
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    Yes, but I do not feel like the categories in UVA are sufficient. Let, I am learning Pell's equations now. Uhunt would list them as problems of GCD/LCM. I was horrified at least three times that how smart people are to solve this problem in a elegant way, until I found there are theory involved.

    And, thanks for your suggestion. People can use both if they want. :)

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8 years ago, # |
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Diophantine Equations 7C

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8 years ago, # |
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Please add to your list this search string:

http://mirror.codeforces.com/problemset/tags/number%20theory?order=BY_SOLVED_DESC

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    8 years ago, # ^ |
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    Thanks for your suggestion. I wanted to add it, but that will defeat my purpose. I want this list to contain problems that fit in a specific category. Note, this list doesn't have to very big. It will contains problems that are almost purely number theoretical.

    One problem with search by tag is, say, a string algorithm problem has a feature that requires a gcd function also. Codeforces will tag this as both string and number theory. But, I do not expect somebody would learn number theory after covering almost all other concepts.

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8 years ago, # |
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A nice number theory problem that includes a bit of probability too: http://mirror.codeforces.com/problemset/problem/711/E

And a CRT problem: http://mirror.codeforces.com/problemset/problem/687/B

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    8 years ago, # ^ |
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    Thanks for your suggestion. 711E looks more like a counting problem. I want to exclude counting problems from number theory problems. If you are sure that it is a number theory problem please suggest the category it belongs to. I don't think I am capable of it ATM.

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      8 years ago, # ^ |
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      Not too sure what you mean by counting problem. This problem is nice and teaches how to apply some basic number theory concepts.

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        8 years ago, # ^ |
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        Ok, I have added 8 categories. Please suggest which category this problem belongs. Should I create another category for it?

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          8 years ago, # ^ |
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          Divisibility/Primes/Co-prime/GCD/LCM i think. Creating categories for problems isn't always that good, since some problems fit more/none.

          Btw in contributors, my name shows as specialist, which triggers me, as my biggest fear in life is too fall to specialist again :D jk

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            8 years ago, # ^ |
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            I don't think it's my fault. I just added your name. Color was automatically added by codeforces :(

            Trying to change your color. What can I do!

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              8 years ago, # ^ |
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              Just remove and add his name again after January 10th, that's when the name color changes are back to normal.

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            8 years ago, # ^ |
            ← Rev. 2   Vote: I like it -7 Vote: I do not like it

            Why do you fear to be in the place you belong?

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            8 years ago, # ^ |
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            I know the feel :|

            Cyan is the most aesthetically beautiful color out of all in CF (in my opinion), but I'd like to have a cyan handle through magic instead of by default :)

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8 years ago, # |
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Problem A is almost an application of CRT. It also requires some other computations, but it is Number Theory.

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8 years ago, # |
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For Primes/GCD/LCM part :

585E - Present for Vitalik the Philatelist

585C - Alice, Bob, Oranges and Apples

LCMSUMH

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8 years ago, # |
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add these also — http://www.spoj.com/problems/NFACTOR/ , http://www.spoj.com/problems/NDIV/ — based on ETF

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8 years ago, # |
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http://mirror.codeforces.com/gym/101212/attachments Problem B from the Bangladesh OI, uses prime factorization.

Two more problems, using logN factorization: 222C - Reducing Fractions and 546D - Soldier and Number Game.

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8 years ago, # |
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There are some really good number-theory problems in e-olymp.

GCD and LCM: 1146 (easy), 1243 (easy), 1147 (normal), 1229 (normal), 1244 (normal), 1230 (hard)

Number systems: 1001 (easy), 1002 (normal), 1008 (normal), 1013 (hard)

Game theory: 1005 (easy), 1009 (normal), 7836 (hard)

Bonus really hard problem: 647 (extreme!)

Hint for 647:
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6 years ago, # |
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Auto comment: topic has been updated by shakil.ahamed (previous revision, new revision, compare).

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