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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 + am (mod 3), and prove that 3|n when the sum of its digits is divisible by 3.
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