Basic Congruences Confusion


by mickles
Tags: basic, confusion, congruences
mickles
mickles is offline
#1
Nov12-12, 04:52 PM
P: 8
Hi, this is not a homework problem, i just have a hard time following the sequence of this

In the book , it shows a couple examples

(=== is the triple equal sign)

1) 26=19+7===3+7===10(mod8)
2) 15=19-4===3-4=-1(mod8)
3)38 = 19*2===3*2=6(mod8)
4) 7===2(mod5), 343=7^3===2^3=8(mod5)

I understand mod8 and whatnot, just how does the book go from 19+7 to 3+7, and from 19-4 to 3-4. I just don't get how 19 and 3 are logically connected

I see how 15===-1(mod8) and 26===10(mod8) and 38=6(mod8).

Any help understanding is appreciated
Phys.Org News Partner Science news on Phys.org
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
Petek
Petek is offline
#2
Nov12-12, 05:39 PM
Petek's Avatar
P: 361
The examples you cited are using the following property of congruences: If [itex]a \equiv b \pmod{m}[/itex], then [itex] a + c \equiv b + c \pmod{m}[/itex]. So, in your first example, let a = 19, b = 3, c = 7 and m = 8.

Does that help?
ramsey2879
ramsey2879 is offline
#3
Nov12-12, 05:46 PM
P: 891
Quote Quote by mickles View Post
Hi, this is not a homework problem, i just have a hard time following the sequence of this

In the book , it shows a couple examples

(=== is the triple equal sign)

1) 26=19+7===3+7===10(mod8)
2) 15=19-4===3-4=-1(mod8)
3)38 = 19*2===3*2=6(mod8)
4) 7===2(mod5), 343=7^3===2^3=8(mod5)

I understand mod8 and whatnot, just how does the book go from 19+7 to 3+7, and from 19-4 to 3-4. I just don't get how 19 and 3 are logically connected

I see how 15===-1(mod8) and 26===10(mod8) and 38=6(mod8).

Any help understanding is appreciated
Any number A === A - N Mod N Thus 19 === 11 === 3 Mod 8, Therefore 19+7 === 3+7 and 19-4 === 3-4.

mickles
mickles is offline
#4
Nov12-12, 05:48 PM
P: 8

Basic Congruences Confusion


Quote Quote by Petek View Post
The examples you cited are using the following property of congruences: If [itex]a \equiv b \pmod{m}[/itex], then [itex] a + c \equiv b + c \pmod{m}[/itex]. So, in your first example, let a = 19, b = 3, c = 7 and m = 8.

Does that help?
Yes that makes a lot more sense now with a,b,c, and m after looking at the theorem.

Thanks for you help
mickles
mickles is offline
#5
Nov12-12, 05:50 PM
P: 8
Quote Quote by ramsey2879 View Post
Any number A === A - N Mod N Thus 19 === 11 === 3 Mod 8, Therefore 19+7 === 3+7 and 19-4 === 3-4.
thank you this also helped


Register to reply

Related Discussions
Basic kinematics confusion all derivatives 0? Introductory Physics Homework 6
Basic kinematics confusion all derivatives 0? Calculus & Beyond Homework 0
basic confusion with eigenvectors Calculus & Beyond Homework 7
Basic Thermo confusion Introductory Physics Homework 15
confusion with very basic algebra General Math 2