Let me first explain my situation here...
I'm a math major and out of all the sciences, physics is my least favorite, but I have to take this science class that forces you to design your own experiments. Math is used in physics all the time, but I have a really hard time connecting math to...
Yeah, we can use uniqueness of prime factorization. We proved it last month, so that's why we can use it. I don't know how to do correct mathematical notation on the computer here, so hopefully you'll understand what I'm typing.
So d=(a,bc). d=(p1^r1)(p2^r2)(p3^r3)... or we can say...
Homework Statement
Let a,b,c be integers. If (b,c)=1, then (a,bc)=(a,b)(a,c)
Homework Equations
This is difficult to answer because some theorems that we haven't proven yet, we can't use.
The Attempt at a Solution
Let g=(a,b) and h=(a,c), g and h are integers.
That means g|a and g|b...
Wait... isn't the problem saying that they are sending 5 0's in hopes that at least one 0 gets received? So, as long as you get one 0, it's like saying "what's the probability that you don't get any 0's?". I'm not understanding why I need to look at the probability that 3, 4, or 5 bits get...
Homework Statement
A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability 0.2. Suppose that we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we...
a=b
oh, oh, oh! That note thing in the instructions... I've been avoiding it the whole time. Just follow it and it's solved... okay, so you said 1 is an object of that property, meaning that step one is finished, step two is to prove that a=b, and then step 2 is finished, meaning the proof...
Well, what I'm saying is that the statement is not true because if r=0 (because r can be any real number and 0 is a real number) then b can be equal to anything, not just one fixed number. b=1, b=2, b=5^.5, whatever, you know? So the statement must be false. That's what I mean with my...
Homework Statement
Prove that there is at most one real number b with the property that br=r for all real numbers r. (Such a number is called a multiplicative identity)
Note: to show there is a unique object with a certain property, show that (1) there is an object with the property and (2)...
Okay, I think I'm getting the general idea. I know that r can only be 0,1,2,3 or 4, but when m is squared, those numbers still have to be lower than five, so 0^2 is less than five, as is 1^2 and 2^2. Am I on the right track?
Aaahhh...
So d=5, k=q, and r=1. Would n=m^2? But how would that help me. I mean if you take the square root then n might not possible be an integer anymore...