Question

Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that...

Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that do not use the prime factorizations of a and b.

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
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b)...
(a) If a and b are positive integers, then show that lcm(a, b) ≤ ab. (b) If a and b are positive integers, then show that lcm(a, b) is a multiple of gcd(a, b).
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...
prove that if gcd(a,b)=1 then gcd (a-b,a+b,ab)=1
prove that if gcd(a,b)=1 then gcd (a-b,a+b,ab)=1
(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).
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.)
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
Prove that if a|n and b|n and gcd(a,b) = 1 then ab|n.
Prove that if a|n and b|n and gcd(a,b) = 1 then ab|n.
Prove that for all non-zero integers a and b, gcd(a, b) = 1 if and only...
Prove that for all non-zero integers a and b, gcd(a, b) = 1 if and only if gcd(a, b^2 ) = 1
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.
Prove Euler’s theorem: if n and a are positive integers with gcd(a,n)=1, then aφ(n)≡1 modn, where...
Prove Euler’s theorem: if n and a are positive integers with gcd(a,n)=1, then aφ(n)≡1 modn, where φ(n) is the Euler’s function of n.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT