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Anonymous Wed 26 Feb 21:21:26 2020 No.11419851 View Reply Original Report

Quoted By: >>11419855 >>11419870 >>11419892 >>11419903 >>11419948 >>11421738

I have an exam on modular arithmetic soon and its kind of filtering me right now, I can't intuit shit like what is the last digit of 9^3453 even though I understand the basic principles of modulo. Any tips?

Anonymous

Anonymous Wed 26 Feb 2020 21:22:50 No.11419855 Report

Quoted By: >>11419857

>>11419851
Just use your intuition bro

Anonymous

Anonymous Wed 26 Feb 2020 21:23:52 No.11419857 Report

Quoted By:

>>11419855
ahhhhhh fuck me, I can't be the lowest common denominator in this class, do they expect us to be fucking Gauss

Anonymous

Anonymous Wed 26 Feb 2020 21:28:11 No.11419870 Report

Quoted By: >>11419884 >>11419887

>>11419851
what are the topics on the exam? if it's digit questions, that's easy. factorise the exponent, build up the individual ones, then multiply it all together

Anonymous

Anonymous Wed 26 Feb 2020 21:32:54 No.11419884 Report

Quoted By:

>>11419870
fuck, i meant break down the exponent into summands, not factorise it

Anonymous

Anonymous Wed 26 Feb 2020 21:33:51 No.11419887 Report

Quoted By: >>11419890 >>11419971 >>11421744

>>11419870
Like Euclid gcd, Bezout Identity, modular arithmetic, rsa, etc. Like prove (2^50)*(3^100)*(5^25) is prime, or how many zeroes are at the end of 1000!

Anonymous

Anonymous Wed 26 Feb 2020 21:34:27 No.11419890 Report

Quoted By: >>11419971

>>11419887
shit i meant prove that number minus one is not prime

Anonymous

Anonymous Wed 26 Feb 2020 21:35:20 No.11419892 Report

Quoted By: >>11419899

>>11419851
9 raised to an even power, last digit is 1
9 raised to odd power, last digit is 9

Anonymous

Anonymous Wed 26 Feb 2020 21:36:30 No.11419899 Report

Quoted By:

>>11419892
Yeah but I'm not strong with the actual breaking it down and proving it with the modular arithmetic is the thing

Anonymous

Anonymous Wed 26 Feb 2020 21:37:01 No.11419903 Report

Quoted By: >>11419908 >>11419911

>>11419851
You fucking retard cunt, you don't Intuit anything, every single one of your exam questions is solved with basic fucking arithmetic. If someone asks you to add 26466443+7448737 without a calculator do you just "gauss" the answer in your head or do you just write out the fucking grade school addition shit and do it digit by digit?

USE PRIME NUMBERS USE MODULAR ARITHMITIC.

9=3*3 and the powers of 3 mod 10 go 3,9,7,1,3,.... so 9^3453=3^6906=3^1mod 10 how fucking hard is that.

Anonymous

Anonymous Wed 26 Feb 2020 21:39:19 No.11419908 Report

Quoted By: >>11419916

>>11419903
I'm retarded, I literally don't understand what you did

Anonymous

Anonymous Wed 26 Feb 2020 21:40:25 No.11419911 Report

Quoted By:

>>11419903
Sorry 3^2 mod 10

Anonymous

Anonymous Wed 26 Feb 2020 21:42:31 No.11419916 Report

Quoted By: >>11419922

>>11419908
do you know what modular arithmetic is? Did you go to literally any of your classes?

Anonymous

Anonymous Wed 26 Feb 2020 21:44:25 No.11419922 Report

Quoted By: >>11421804 >>11422815

>>11419916
yes I did
why is 6909 equal to 2 mod 10, isnt it equal to 9 mod 10

Anonymous

Anonymous Wed 26 Feb 2020 21:50:51 No.11419948 Report

Quoted By:

>>11419851
1. start computing the first few powers of 9 mod 10.
2. find out that 9^2 = 1 mod 10
3. deduce that 9^k depends only on k mod 2
4. 3453 = 1 mod 2
5. conclude 9^3453 = 9^1 = 9 mod 10

Anonymous

Anonymous Wed 26 Feb 2020 22:01:31 No.11419971 Report

Quoted By: >>11419981

>>11419887
>>11419890
just out of curiosity, is your course based on Stillwell's "Elements of Number Theory"?
gcd and Bezout are very easy, gcd is elementary school-level arithmetic and Bezout is just working your way up from the result of it. just brush up on basic modular arithmetic, Fermat's little theorem, Euler's function, and the RSA algorithm and you'll be fine

Anonymous

Anonymous Wed 26 Feb 2020 22:05:56 No.11419981 Report

Quoted By:

>>11419971
It's based on Magdon-Ismail "Discrete Mathematics and Computing"
and thanks

Anonymous

Anonymous Thu 27 Feb 2020 15:14:51 No.11421738 Report

Quoted By:

>>11419851
Compute consecutive powers of 9 and see if there's a pattern to the last digit. In this case there is and it just goes back and forth between 1 and 9 which you can use to compute 9^3453. A similar trick works for other powers.

Anonymous

Anonymous Thu 27 Feb 2020 15:18:53 No.11421744 Report

Quoted By:

>>11419887
1000! has 1000, 100, and 10. so i guess 6 zeroes

but ah it has all those 5s and 2s. so half of each

Anonymous

Anonymous Thu 27 Feb 2020 15:49:16 No.11421804 Report

Quoted By:

>>11419922
No. The repetition of powers of 3 is every 4 times, not every 10. That part isn't mod 10.

Anonymous

Anonymous Thu 27 Feb 2020 21:50:22 No.11422815 Report

Quoted By:

>>11419922
6906 not 6909

Anonymous

Anonymous Fri 28 Feb 2020 17:05:10 No.11424851 Report

Quoted By:

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