Question

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.

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
(7) Which of the following statement is TRUE? (A) If am−1 ≡ 1 (mod m), then...
(7) Which of the following statement is TRUE? (A) If am−1 ≡ 1 (mod m), then by Fermat’s Little Theorem m must be a prime. (B) If ac ≡ bc (mod m), then a ≡ b (mod m). (C) If a ≡ b (mod m) and n | m, then a ≡ b (mod n). (D) If 2n −1 is a prime, then 2n−2(2n −1) is a perfect number. (E) If p is a prime, then 2p −1 is also...
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).
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. (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: 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.
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...
Let p be be prime and p ≡ 1 (mod 4|a|). Prove that a is a...
Let p be be prime and p ≡ 1 (mod 4|a|). Prove that a is a quadratic residue mod p.
Let p be a prime that is congruent to 3 mod 4. Prove that there is...
Let p be a prime that is congruent to 3 mod 4. Prove that there is no solution to the congruence x2≡−1 modp. (Hint: what would be the order of x?)
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.
use the fundamental theorem of arithmetic to prove: if a divides bc and gcd(a,b)=1 then a...
use the fundamental theorem of arithmetic to prove: if a divides bc and gcd(a,b)=1 then a divides c.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT