Algebra Pre-Algebra and Basic Algebra Math Forum

 September 21st, 2014, 01:04 PM #1 Newbie   Joined: Sep 2014 From: Canada Posts: 4 Thanks: 0 Modulos Please help me solve this problem Problem 1 Let: (A=1, B=2, C=3,.., Z=26) a) What is (A + N) mod 26 in this system? b) What is (B + 6) mod 26 in this system? c) What is (Y - 4) mod 26 in this system? d) What is (C - 9) mod 26 in this system? Problem 2 a) The remainder of any positive integer when divided by 100 is the integer made of the two rightmost digits. b) The remainder of any positive integer when divided by 1000 is the integer made of the three rightmost digits. c) If a ≡ x1 (mod m) and b ≡ y1 (mod m), then we will have ab ≡ x1y1 (mod m). True or False?
 September 21st, 2014, 01:50 PM #2 Math Team   Joined: Apr 2010 Posts: 2,778 Thanks: 361 1.) a.) A + N = 1 + 14 ≡ 15 mod 26 in this system. b.) To what value is B equal to? c.) To what value is Y equal to? d.) To what value is C equal to? You may want to add 26. 2.) a.) Any integer is of the form 100 * k + r where k is any integer and r are the two rightmost digits. b.) Can you do something similar as for a.)? c.) Let a = k * m + x1 and Let b = l * m + y1. Can you compute a * b mod m?
 September 21st, 2014, 07:19 PM #3 Newbie   Joined: Sep 2014 From: Canada Posts: 4 Thanks: 0 Thank you very much
 January 31st, 2018, 05:51 PM #4 Newbie   Joined: Jan 2018 From: Toronto Posts: 12 Thanks: 0 Similar questions - Remainder of a positive integer when divided by 100 I have the same question expect I don't know why - the explanation which is required for my homework. Please assist. The remainder of any positive integer when divided by 100 is the integer made of the two rightmost digits. True or False and why? - I answered True, but I don't know why. I have been searching online to understand the concept of why it is made of two rightmost dights.
 January 31st, 2018, 05:53 PM #5 Newbie   Joined: Jan 2018 From: Toronto Posts: 12 Thanks: 0 Also, I don't understand this question - Please help me understand why it is true or false. If a ≡ x1 (mod m) and b ≡ y1 (mod m), then we will have ab ≡ x1y1 (mod m). True or False and why? Thank you.
January 31st, 2018, 06:00 PM   #6
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,730
Thanks: 602

Math Focus: Yet to find out.
Quote:
 Originally Posted by Tricia I have the same question expect I don't know why - the explanation which is required for my homework. Please assist.
You might have better luck making a new post of your own. By all means, if this thread is relevant, you can link it in your post.

January 31st, 2018, 06:55 PM   #7
Senior Member

Joined: Oct 2013
From: New York, USA

Posts: 619
Thanks: 83

Quote:
 Originally Posted by Tricia Also, I don't understand this question - Please help me understand why it is true or false. If a ≡ x1 (mod m) and b ≡ y1 (mod m), then we will have ab ≡ x1y1 (mod m). True or False and why? Thank you.
If I understand, it's saying x and y are both multiples of m, which makes xy a multiple of m, which makes the statement true.

January 31st, 2018, 07:14 PM   #8
Senior Member

Joined: Aug 2012

Posts: 2,075
Thanks: 593

Quote:
 Originally Posted by Tricia I have the same question ....
Are you both in the same class?

I think the hard part of this problem is to figure out which ordinal position each letter is. I have to start at abc and count on my fingers.

 February 1st, 2018, 09:19 AM #9 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Since A= 1 and Z= 26, by "counting on my fingers" (literally!) N= 14. (a) What is (A + N) mod 26 in this system? Whatever number "N" is in this system. Since A= 1. "A+ N" is the very next letter, "O". b) What is (B + 6) mod 26 in this system? Counting forward from B six places, C, D, E, F, G, H. (B+ 6)= H (mod 26) c) What is (Y - 4) mod 26 in this system? Going back from Y four places, X, W, V, U. (Y- 4)= U (mod 26) d) What is (C - 9) mod 26 in this system? "mod" is cyclic. 3- 9= -6= 26- 6= 20 (mod 26) and the 20th letter is T. Or, starting from C and going back 9 places, B, A, Z, Y, X, W, V, U, T. C- 9= T (mod 26) Thanks from Tricia
February 1st, 2018, 09:26 AM   #10
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

Quote:
 Originally Posted by Tricia Also, I don't understand this question - Please help me understand why it is true or false. If a ≡ x1 (mod m) and b ≡ y1 (mod m), then we will have ab ≡ x1y1 (mod m). True or False and why? Thank you.
"a ≡ x1 (mod m)" means a= x1+ km for some integer k.
"b ≡ y1 (mod m)" means b= y1+ pm for some integer p.

So ab= (x1+ km)(y1+ pm)= x1y1+ x1pm+ kmy1+ kpm^2= x1y1+ m(x1+ ky1+ kpm) which is "x1y1+ m times an integer" so is x1y1 (mod m).

 Tags modulos, problem, solve

,

### if a ≡ x1 (mod m) and b ≡ y1 (mod m), then we will have ab ≡ x1y1 (mod m)

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post ternczy Calculus 1 January 31st, 2014 11:01 AM Noideawhatimdoing Algebra 4 November 8th, 2013 09:07 PM salgat Number Theory 2 February 18th, 2010 03:45 PM POW1Q Algebra 1 January 27th, 2010 08:53 PM SidT Calculus 2 June 6th, 2009 06:11 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top