Question

Prove that if ? ≡ ? (mod n) and ? ≡ ? (mod n), then ?...

Prove that if ? ≡ ? (mod n) and ? ≡ ? (mod n), then ? ≡ ? (mod n). This proves that congruence mod n is transitive.

and

: Prove that if ? ≡ ? (mod n) and ? ≡ ? (mod n), then

  1. a) ? + ? ≡ ? + ? (mod n)

  2. b) ?? ≡ ?? (mod n)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
prove that n> 1 and (n-1)!congruence -1(mod n) then n is prime
prove that n> 1 and (n-1)!congruence -1(mod n) then n is prime
9e) fix n ∈ ℕ. Prove congruence modulo n is an equivalence relation on ℤ. How...
9e) fix n ∈ ℕ. Prove congruence modulo n is an equivalence relation on ℤ. How many equivalence classes does it have? 9f) fix n ∈ ℕ. Prove that if a ≡ b mod n and c ≡ d mod n then a + c ≡b + d mod n. 9g) fix n ∈ ℕ.Prove that if a ≡ b mod n and c ≡ d mod n then ac ≡bd mod n.
Prove: Proposition 11.13. Congruence modulo n is an equivalence relation on Z : (1) For every...
Prove: Proposition 11.13. Congruence modulo n is an equivalence relation on Z : (1) For every a ∈ Z, a = a mod n. (2) If a = b mod n then b = a mod n. (3) If a = b mod n and b = c mod n, then a = c mod n
Prove that n is prime iff every linear equation ax ≡ b mod n, with a...
Prove that n is prime iff every linear equation ax ≡ b mod n, with a ≠ 0 mod n, has a unique solution x mod n.
a) Prove: If n is the square of some integer, then n /≡ 3 (mod 4)....
a) Prove: If n is the square of some integer, then n /≡ 3 (mod 4). (/≡ means not congruent to) b) Prove: No integer in the sequence 11, 111, 1111, 11111, 111111, . . . is the square of an integer.
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 for n ≥ 5, (n−1)! ≡ 0 mod n if and only if n...
Prove that for n ≥ 5, (n−1)! ≡ 0 mod n if and only if n is composite. (Take care to consider why your argument would not work for n ≤ 4. . . )
Prove: If n ≡ 3 (mod 8) and n = a2 + b2 + c2 +...
Prove: If n ≡ 3 (mod 8) and n = a2 + b2 + c2 + d2, then exactly one of a, b, c, d is even. (Hint: What can each square be modulo 8?)
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0...
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0 (mod n), then a ≡ 0 (mod n) or b ≡ 0 (mod n). (b) Prove or disprove: Suppose p is a positive prime. If ab ≡ 0 (mod p), then a ≡ 0 (mod p) or b ≡ 0 (mod p).
Prove the Basic Principal of Difference of squares: If x2 ≡ y2 (mod n) and x...
Prove the Basic Principal of Difference of squares: If x2 ≡ y2 (mod n) and x is not ± y, where x and y lie in the range {0, … , n-1}, then n is composite and has gcd(x-y, n) as a non-trivial factor.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT