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Hey Cig Daze and other math wizards..?
- Thread starter DollaBill
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clayinaustin
Charter Member
Here's a better question... Why should we care? 
phragle
Charter Member
How did we go from discussing math to hotel sheets??
DollaBill
New member
everything hits the gutter quickly LOL. I'm curious
Perlmudder
New member
DAREDEVIL
Banned
DAMN,,,thats way more then 4X the mess i thought !!!!! LOL:sifone:
This is going back a ways, but basically the quadratic residue can be considered a remainder, or what's left over.
It's from an abstract form of modular integer arithmetic. the closest common examples I can think of to explain the concept are numerical schemes like binary, hexadecimal, octadecimal bit math, or something more familiar to us is 12 hour clocks.
These are all schemes using something other than base 10 (normal math is base 10, i.e. 1,2,3,4,5,6,7,8,9,10,11(1x10 + 1), 12(1x10 + 2), and so on. After you reach 10, the numbers repeat. Binary is base 2, Hexadecimal is base 6, etc.
For instance let's look at the clock which is base 12.
This can most easily be understood by saying it's 9 o'clock and you add 6 hours. Logically, you'd think it should be 15 o'clock...no, it's 3 o'clock because we hit 12, and then we repeat. 3 would be the residue it we were talking about "linear residue base (moduli, or mod) 12"
Now, lets get back to the quadratic part. Quadratic is a polynomial equation to the 2nd order. f(x) = mx^2+b
The independent variable is to the second power, or squared (squared = quad)
When referring to quadratic residue, in a modular system, we're in a realm of remainders of squares (like the clock, but non-linear, it's now squared), so instead of counting 1,2,3,4,5..., if we use [mod 2] it would be 2,4,6,8..., if we use [mod 3] we have 3,6,9,12..., and so on.
The expression is as follows [q is quadratic residue]:
q = X^2 (mod n)
So, mod (or moduli) is the base system modifier.
Let's say x is 3 and I want to evaluate it to mod 2
3^2 = 9; and if I use mod 2 (2,4,6,8) I can express this as 4x2 + 1
q=1 because the +1 from above is the residue or remainder after I count by 2's
Another example:
4^2 (mod 7)
4 squared is 16.
If I count by 7's....I go 7,14, 21...etc.
q=2 because I would express this as 2x7 + 2 to get 16.
Hope that makes sense.
It's from an abstract form of modular integer arithmetic. the closest common examples I can think of to explain the concept are numerical schemes like binary, hexadecimal, octadecimal bit math, or something more familiar to us is 12 hour clocks.
These are all schemes using something other than base 10 (normal math is base 10, i.e. 1,2,3,4,5,6,7,8,9,10,11(1x10 + 1), 12(1x10 + 2), and so on. After you reach 10, the numbers repeat. Binary is base 2, Hexadecimal is base 6, etc.
For instance let's look at the clock which is base 12.
This can most easily be understood by saying it's 9 o'clock and you add 6 hours. Logically, you'd think it should be 15 o'clock...no, it's 3 o'clock because we hit 12, and then we repeat. 3 would be the residue it we were talking about "linear residue base (moduli, or mod) 12"
Now, lets get back to the quadratic part. Quadratic is a polynomial equation to the 2nd order. f(x) = mx^2+b
The independent variable is to the second power, or squared (squared = quad)
When referring to quadratic residue, in a modular system, we're in a realm of remainders of squares (like the clock, but non-linear, it's now squared), so instead of counting 1,2,3,4,5..., if we use [mod 2] it would be 2,4,6,8..., if we use [mod 3] we have 3,6,9,12..., and so on.
The expression is as follows [q is quadratic residue]:
q = X^2 (mod n)
So, mod (or moduli) is the base system modifier.
Let's say x is 3 and I want to evaluate it to mod 2
3^2 = 9; and if I use mod 2 (2,4,6,8) I can express this as 4x2 + 1
q=1 because the +1 from above is the residue or remainder after I count by 2's
Another example:
4^2 (mod 7)
4 squared is 16.
If I count by 7's....I go 7,14, 21...etc.
q=2 because I would express this as 2x7 + 2 to get 16.
Hope that makes sense.
DollaBill
New member
Aren't winters in the northeast great?!
god don't remind me.
Cash Bar
Charter Member
Why not do like all the other inmates and study Islam or Buhdism(?). :rofl::willy_nilly:
DollaBill
New member
lol
MarylandMark
Charter Member
Close this thread- I have a hangover and feel dumber since I don't know fancy math talk
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