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
icon
Related questions
Question

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. 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Ring
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,