# Confusion regarding symbol

• Nov 22nd 2010, 01:02 PM
gregarion
Confusion regarding symbol
Hey guys , i am unclear regarding a symbol which i encountered in my work. I was given a question in which they state a few algorithm. The part which i am confused about is when they told me to use a variable named q where q|P -1 . P is also a variable , but a prime number.

What i am confused about is what does "|" mean?

1) Does it mean that q = P -1 , which means to say if P is 11 , q is 10?

2) Does it mean that q can be any number which is less then P -1 ? If P = 11 , then q can be from 1 till 10.

Or am i completely wrong in understanding what "|" does? Hope for some clarification. Thank you.
• Nov 22nd 2010, 01:08 PM
dwsmith
$\displaystyle \displaystyle q|P-1 \ \mbox{means} \ q*x=P-1$

• Nov 22nd 2010, 01:11 PM
gregarion
Hey , thank for the reply. Im not sure if i understand what u mean , but let me try explaining to you what i see and hope you can tell me if i am right.

Basically , when q * x , the value of it is suppose to be P - 1? What is x and how do we go about to get it?
• Nov 22nd 2010, 01:15 PM
Plato
$\displaystyle q|(p-1)$ reads "q divides p-1".
• Nov 22nd 2010, 01:17 PM
dwsmith
$\displaystyle x\in\mathbb{Z}$

Looking at your example of p=11 we get x by:

$\displaystyle q*x=11-1\rightarrow q*x=10 \ \mbox{and since q is prime} \ q=2,5\rightarrow 2*x=10 \ \mbox{or} \ 5*x=10$ Thus, x = 5 or 2
• Nov 22nd 2010, 01:22 PM
gregarion
okay , so what i means that the value of q is based on the value of (p - 1)?

So , for example if p = 11 , then q should be 10 as 10|(p - 1) = 1?
• Nov 22nd 2010, 01:22 PM
dwsmith
q is prime so q isn't 10 but q*x=10 where q can be 2 or 5 which are prime numbers.
• Nov 22nd 2010, 01:24 PM
dwsmith
Quote:

Originally Posted by gregarion
10|(p - 1) = 1?

This shouldn't have an equal sign.

$\displaystyle 10|(p-1)\rightarrow 10*x=p-1$ The equal sign is built into the divides notation.
• Nov 22nd 2010, 01:37 PM
gregarion
Okay , q always has to be a prime? Let me see if i get it .

P = 281
q|(P-1) = 280

Factors of 280 = 2 * 2 * 2 * 5 * 7

Thus , q can be either 2, 5 or 7?

Sorry , 10|(p - 1) = 1 was suppose to mean that when 10 is divided by (p-1) , the value should be 1.
• Nov 22nd 2010, 01:38 PM
dwsmith
I miss read your sentence. q doesn't have to be prime. But you seem to have figured out how to solve it now. Just pick a q*x which equals P-1.
• Nov 22nd 2010, 01:43 PM
gregarion
okay , so if q is not a prime , then when P = 280 and q is based on q|P-1 , thus q can be 280 then? as it fulfills the requirement of it having to be equals P -1.
• Nov 22nd 2010, 01:45 PM
dwsmith
Yup. Then x=1.
• Nov 22nd 2010, 01:47 PM
gregarion
Thanks a lot for the clarification !