What does the whole modulo thing actually mean? Watch

claret_n_blue
Badges: 16
Rep:
?
#1
Report Thread starter 7 years ago
#1
I have to solve for x so two linear congruences are equal, but what does A = B mod C actually mean?

Also, how would I solve it? The question is:

x = A mod B
x = C mod D


and I have to find the smallest integer for x which satisfies these to linear congruences simultaneously.

How do I do this?

Thank you
0
reply
nuodai
Badges: 14
#2
Report 7 years ago
#2
If you write a \equiv b \pmod c it means that when you divide a by c you get the same remainder as when you divide b by c. That is, a=q_1c+r and b=q_2c+r. Equivalently, a-b is divisible by c.

So you need to find x such that x-A is a multiple of B and x-C is a multiple of D.
reply
j.alexanderh
Badges: 14
Rep:
?
#3
Report 7 years ago
#3
a=b (mod c) means a=kc+b, where k is a constant. Basically, it is the remainder when a is divided by c.

You can solve systems of two congruences using the Chinese remainder theorem. If you only need one solution, which you do, then you can write down the solutions for the first congruence until you find one which satisfies the second one (as long as the numbers involved are fairly small).
0
reply
claret_n_blue
Badges: 16
Rep:
?
#4
Report Thread starter 7 years ago
#4
(Original post by j.alexanderh)
a=b (mod c) means a=kc+b, where k is a constant. Basically, it is the remainder when a is divided by c.

You can solve systems of two congruences using the Chinese remainder theorem. If you only need one solution, which you do, then you can write down the solutions for the first congruence until you find one which satisfies the second one (as long as the numbers involved are fairly small).
So does that mean something like: 8 = 2 mod 3, because, using the a=kc +b formula, 8 = 3k + 2, where k=2, right?

What do you mean the numbers are fairly small? Less than 10,20?
0
reply
j.alexanderh
Badges: 14
Rep:
?
#5
Report 7 years ago
#5
(Original post by claret_n_blue)
So does that mean something like: 8 = 2 mod 3, because, using the a=kc +b formula, 8 = 3k + 2, where k=2, right?

What do you mean the numbers are fairly small? Less than 10,20?
Yeah, the first part is right. I should have mentioned that k is an integer.

Fairly small in this case means you can write the first ten or fifteen multiples of the number without any effort, and quickly check the remainders of these numbers. I t depends on how good your arithmetic is, but this method should be sufficient for numbers larger than twenty. Just don't try it if the numbers are 1024=175 mod whatever.
0
reply
claret_n_blue
Badges: 16
Rep:
?
#6
Report Thread starter 7 years ago
#6
(Original post by j.alexanderh)
Yeah, the first part is right. I should have mentioned that k is an integer.

Fairly small in this case means you can write the first ten or fifteen multiples of the number without any effort, and quickly check the remainders of these numbers. I t depends on how good your arithmetic is, but this method should be sufficient for numbers larger than twenty. Just don't try it if the numbers are 1024=175 mod whatever.
Cool, thanks

I'm going through stuff on the Chinese remainder theorem now, so if I get stuck, hopefully you won't mind me posting more questions

Thanks once more
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Aston University
    Postgraduate Open Day Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19

Brexit: Given the chance now, would you vote leave or remain?

Remain (907)
79.98%
Leave (227)
20.02%

Watched Threads

View All
Latest
My Feed