Saturday

September 20, 2014

September 20, 2014

Posted by **Samantha** on Saturday, December 4, 2010 at 3:21pm.

- Discrete Math -
**MathMate**, Saturday, December 4, 2010 at 7:45pmGiven:

a≡c mod n

b≡d mod n

Prove that (a-c)≡(b-d) mod n.

Let

a=kn+r ... k,r ∈ ℤ^{+}

c=ln+r ... l,r ∈ ℤ^{+}

Subtract:

(a-c)=(k-l)n

Similarly,

(b-d)=(p-q)n ... p,q ∈ ℤ^{+}

Therefore

(a-c)≡(b-d) mod n

**Answer this Question**

**Related Questions**

Proofs and numbers - Prove the following theorem: Suppose p is a prime number, r...

DISCRETE MATHS - Prove that if n is an odd positive integer, then 1 ≡ n2 (...

Discrete Mathematics - Prove that if n is an odd positive integer, then 1 ≡...

discrete math - 1)prove that if x is rational and x not equal to 0, then 1/x is ...

Discrete Math - Theorem: For every integer n, if x and y are positive integers ...

another college math question - Please teach me. I am completely blank with it...

Discrete Math - 1. Assume that n is a positive integer. Use the proof by ...

discrete math - list five integers that are congruent to 4 modulo 12 4, 16, 36...

discrete math - Let f:ℤ+ → ℤ+ be the function defined by: for...

discrete math - 5= (1+4) (1+4)^n= 1^n + 2*1*4 + ...+4^n which is 1 mod 4 Prove ...