Question

(a) Show that if gcd(a, m) > 1 that there exists [b] 6= [0] with [a][b]...

(a) Show that if gcd(a, m) > 1 that there exists [b] 6= [0] with [a][b] = [0] (we say that [a] is a zero divisor ). (b) Use this to show that if gcd(a, m) > 1 then [a]m is not a unit.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is...
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is the largest number that divides both a and b. One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax+by for x, y ∈ N. We say that a and b are relatively prime iff gcd(a, b) = 1. Prove that a and n are relatively prime if and...
Given that the gcd(a, m) =1 and gcd(b, m) = 1. Prove that gcd(ab, m) =1
Given that the gcd(a, m) =1 and gcd(b, m) = 1. Prove that gcd(ab, m) =1
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a,...
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) = 1. (Hint: use the GCD characterization theorem.) (b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (Hint: you can use the GCD characterization theorem again but you may need to multiply equations.) (c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if and...
1. Show that gcd(1137, -419) = gcd (1137, 419) = gcd (419, 299) = gcd (299,...
1. Show that gcd(1137, -419) = gcd (1137, 419) = gcd (419, 299) = gcd (299, 120)= gcd (120, 59). Can you use this to compute gcd(1137, -419)? 2. Show that the gcd(n,n+1)=1 for all n∈Z. 3. Calculate gcd(181451, 186623).
Show that gcd(a + b, lcm(a, b)) = gcd(a, b) for all a, b ∈ Z.
Show that gcd(a + b, lcm(a, b)) = gcd(a, b) for all a, b ∈ Z.
(a) If a and b are positive integers, then show that gcd(a, b) ≤ a and...
(a) If a and b are positive integers, then show that gcd(a, b) ≤ a and gcd(a, b) ≤ b. (b) If a and b are positive integers, then show that a and b are multiples of gcd(a, b).
Assume that gcd(a, m) = 1, gcd(a, n) = 1, and gcd(m, n) = 1. Assume...
Assume that gcd(a, m) = 1, gcd(a, n) = 1, and gcd(m, n) = 1. Assume that a has order s modulo m and order t modulo n. What is the order of a modulo mn? Prove that your answer is correct
How can I prove that if a>b>0, gcd(a,b) = gcd(a-b,b)
How can I prove that if a>b>0, gcd(a,b) = gcd(a-b,b)
1. (a) Let a, b and c be positive integers. Prove that gcd(ac, bc) = c...
1. (a) Let a, b and c be positive integers. Prove that gcd(ac, bc) = c x gcd(a, b). (Note that c gcd(a, b) means c times the greatest common division of a and b) (b) What is the greatest common divisor of a − 1 and a + 1? (There are two different cases you need to consider.)
Prove that if gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1.
Prove that if gcd(a,b)=1 and c|(a+b), then gcd(a,c)=gcd(b,c)=1.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT