Question

Let d1= gcd(a,b) and d2=gcd(b,r). Prove that d1=d2 by d2<= d1 and d1<=d2

Let d1= gcd(a,b) and d2=gcd(b,r). Prove that d1=d2 by d2<= d1 and d1<=d2

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

Homework Answers

Answer #1

So if and so as is the greatest common divisor

Similarly we have

So that as is the greatest common divisor

Combining these we get

That is,

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

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
let f:A->B and let D1, D2, and D be subsets of A. Prove or Disprove F^-1(D1UD2)=F^-1(D1)UF^-1(D2)
let f:A->B and let D1, D2, and D be subsets of A. Prove or Disprove F^-1(D1UD2)=F^-1(D1)UF^-1(D2)
1. Let D1 and D2 be two open disks in R^2 whose closures D1 and D2...
1. Let D1 and D2 be two open disks in R^2 whose closures D1 and D2 intersect in exactly one point, so the boundary circles of the two disks are tangent. Determine which of the following subspaces of R 2 are connected: (a) D1 ∪ D2 . (b) D1 ∪ D2 . (c) D1 ∪ D2 .
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...
Let d1 = 2, d2 = 3, and dn = dn−1 · dn−2. Find an explicit...
Let d1 = 2, d2 = 3, and dn = dn−1 · dn−2. Find an explicit formula for dn in terms of n and prove that it works.
Let P = (x1, d1) -> (x2, d2) and Q = (x2, d2) -> (x3, d3)....
Let P = (x1, d1) -> (x2, d2) and Q = (x2, d2) -> (x3, d3). P and Q are covering maps. Show that the composition of P and Q (P ◦ Q) is also a covering map from (x1, d1) to (x3, d3). Thank you!
9. Let a, b, q be positive integers, and r be an integer with 0 ≤...
9. Let a, b, q be positive integers, and r be an integer with 0 ≤ r < b. (a) Explain why gcd(a, b) = gcd(b, a). (b) Prove that gcd(a, 0) = a. (c) Prove that if a = bq + r, then gcd(a, b) = gcd(b, r).
Let |a| = n. Prove that <a^i> = <a^j> if and only if gcd(n,i) = gcd...
Let |a| = n. Prove that <a^i> = <a^j> if and only if gcd(n,i) = gcd (n,j) and |a^i| = |a^j| if and only if gcd(n,i) = gcd(n,j).
Prove that if a > b then gcd(a, b) = gcd(b, a mod b).
Prove that if a > b then gcd(a, b) = gcd(b, a mod b).
Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod...
Let gcd(m1,m2) = 1. Prove that a ≡ b (mod m1) and a ≡ b (mod m2) if and only if (meaning prove both ways) a ≡ b (mod m1m2). Hint: If a | bc and a is relatively prime to to b then a | c.
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.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT