Question

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

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

Homework Answers

Answer #1

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

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
Prove: Let n ∈ N, a ∈ Z, and gcd(a,n) = 1. For i,j ∈ N,...
Prove: Let n ∈ N, a ∈ Z, and gcd(a,n) = 1. For i,j ∈ N, aj ≡ ai (mod n) if and only if j ≡ i (mod ordn(a)). Where ordn(a) represents the order of a modulo n. Be sure to prove both the forward and backward direction.
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.
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...
Suppose we already proved the correctness of the RSA algorithm under the assumption that gcd(m, n)...
Suppose we already proved the correctness of the RSA algorithm under the assumption that gcd(m, n) = 1. Prove the correctness of the RSA algorithm without this assumption, that is, m^de ≡ m (mod n) for all 1 ≤ m < n. (Hint: use the Chinese remainder theorem.)
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.
needed in c++ (no step by step) The gcd(m, n) can also be defined recursively as...
needed in c++ (no step by step) The gcd(m, n) can also be defined recursively as follows: If m % n is 0, gcd (m, n) is n. Otherwise, gcd(m, n) is gcd(n, m % n). Write a recursive function to find the GCD. Write a test program that prompts the user to enter two integers and displays their GCD.
14. Assume that n is a nonnegative integer . a . Find gcd ( 2n +...
14. Assume that n is a nonnegative integer . a . Find gcd ( 2n + 1 , n )
Let a be an element of order n in a group and d = gcd(n,k) where...
Let a be an element of order n in a group and d = gcd(n,k) where k is a positive integer. a) Prove that <a^k> = <a^d> b) Prove that |a^k| = n/d c) Use the parts you proved above to find all the cyclic subgroups and their orders when |a| = 100.
Let n be a positive odd integer, prove gcd(3n, 3n+16) = 1.
Let n be a positive odd integer, prove gcd(3n, 3n+16) = 1.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT