30. Prove that any positive integer is congruent to its units digit modulo 10. 31. If a = b (mod n), prove that a" = bm (mod n) for every positive integer m. 32. Prove that if m is an integer, then either m2 = 0 (mod 4) or m2 = 1 (mod 4) Consider the cases where m is even and where m is odd.)

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

Please help with number 31. 

30. Prove that any positive integer is congruent to its units digit modulo 10.
31. If a = b (mod n), prove that a" = bm (mod n) for every positive integer m.
32. Prove that if m is an integer, then either m2 = 0 (mod 4) or m² = 1 (mod 4)
Consider the cases where m is even and where m is odd.)
Transcribed Image Text:30. Prove that any positive integer is congruent to its units digit modulo 10. 31. If a = b (mod n), prove that a" = bm (mod n) for every positive integer m. 32. Prove that if m is an integer, then either m2 = 0 (mod 4) or m² = 1 (mod 4) Consider the cases where m is even and where m is odd.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Simulation
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,