# Discrete Math

posted by .

Let a, b, c, and d be integers, and let n be a positive integer. Prove that if a is congruent to c mod n and b is congruent to d mod n, then (a-b) is congruent to (c-d) mod n

• Discrete Math -

Given:
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

## Similar Questions

1. ### A number thoery question

Please help me! Thank you very much. Prove Fermat's Last theorem for n=3 : X^3 + Y^3 = Z^3 where X, Y, Z are rational integers, then X, Y, or Z is 0. Hint: * Show that if X^3 + Y^3 = Epsilon* Z^3, where X, Y, Z are quadratic integers …
2. ### another college math question

Please teach me. I am completely blank with it. :( Let alpha = (3+sqrt(-3))/2 belongs to Q[sqrt(3)]. Show that if x is congruent to 1 mod alpha, then x^3 is congruent to 1 (mod alpha)^3. Similarly, show that if x is congruent to -1 …
3. ### number theory

give an example to show that a^2 congruent to b^2 mod n need not imply that a congruent to b mod n.
4. ### Geometry

Reflective sets of angles Given: <ABC is congruent to <EFG <1 is congruent to <3 Prove: <2 is congruent to <4 Statements: Reasons: 1.) <ABC is congruent to <EFG 1.) Given (m<ABC is congruent to m<EFG) …
5. ### GEOMETRY

Reflective sets of angles Given: <ABC is congruent to <EFG <1 is congruent to <3 Prove: <2 is congruent to <4 Statements: Reasons: 1.) <ABC is congruent to <EFG 1.) Given (m<ABC is congruent to m<EFG) …
6. ### math

Prove eachh mathematical statement for integers m,n,k,p,a,b 12. For every prime p and nonzero n we have n^2 is congruent to nMODp if and only if either n is congruent to 1MODp or n is congruent to 0MODp.
7. ### math

Which two is true as i'm confused A) 3+7 ß 10 mod 15 17 + 9 ß 4 mod 21 12 + 14 ß 0 mod 26 B) 4+11 ß 2 mod 13 9+7 ß 4 mod 12 13 + 13 ß 1 mod 25 C) 5+9 ß 4 mod 10 16 + 13 ß 3 mod 26 12 + 7 ß 6 mod 14 d)2+7 …
8. ### Geometry

PQR is congruent to DJE. complete the statement below PR is congruent to __, DJ is congruent to __ angle E is congruent to __ 1) PR is congruent to PQ, DJ is congruent to PQ, angle E is congruent to angle R 2) PR is congruent to DE, …
9. ### Proofs and numbers

Prove the following theorem: Suppose p is a prime number, r, s are positive integers and x is an arbitrary integer. Then we have x^r identical to x^s (mod p) whenever r is identical to s (mod 11).for x belongs to an integer
10. ### geometry

Given: AC perpendicular BD and AB congruent CB. Prove AD congruent CD. It is a kite figure. I need statements and reasons. Problem states Plan: prove triangle ABE congruent CBE. The use congruent corresponding parts AE and CE to show …

More Similar Questions