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Basic Congruences Confusion 
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#1
Nov1212, 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=194===34=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 194 to 34. 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 


#2
Nov1212, 05:39 PM

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? 


#3
Nov1212, 05:46 PM

P: 894




#4
Nov1212, 05:48 PM

P: 8

Basic Congruences Confusion
Thanks for you help 


#5
Nov1212, 05:50 PM

P: 8




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