a) Find a0, a1, a2, a3 so that 1234 = a3 · 10^3 + a2 · 10^2 + a1 · 10^1 + a0 · 10^0 b) Prove that 10^k ≡ 1 (mod 3) for all k ∈ Z with k ≥ 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 55RE
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How do I do this:

a) Find a0, a1, a2, a3 so that 1234 = a3 · 10^3 + a2 · 10^2 + a1 · 10^1 + a0 · 10^0

b) Prove that 10^k ≡ 1 (mod 3) for all k ∈ Z with
k ≥ 0.

c) Let am, am-1, ... , a1, a0 be the digits (listed from left to right) of some integer n ∈ Z. Prove that n ≡ a0 + a1 + a2 + ... + am-1 + a(mod 3), and prove that 3|n when the sum of its digits is divisible by 3. 

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