SOLUTION: Let a, b, n ∈ Z with n > 1. Prove that if a ≡ b (mod n) then 2a ≡ 2b (mod n)

Algebra ->  Proofs -> SOLUTION: Let a, b, n ∈ Z with n > 1. Prove that if a ≡ b (mod n) then 2a ≡ 2b (mod n)       Log On


   

Question 1042856: Let a, b, n ∈ Z with n > 1. Prove that if a ≡ b (mod n) then 2a ≡ 2b (mod n)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a = b (mod n) is the same as saying a-b = k*n where k is some integer.

Multiply both sides of a-b = k*n by 2 to get 2a-2b = 2kn

2a-2b = 2kn can be then written in the form 2a = 2b (mod n). So that wraps up the proof.