3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.

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
3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.
Hint: considering splitting into cases where integers are of the form a·k+b or (a.k+b)
for ke N where a and b are fixed for a given case, b varies over the cases and the least
significant digit of the integer depends on only b.
Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respec-
tively.
Transcribed Image Text:3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6. Hint: considering splitting into cases where integers are of the form a·k+b or (a.k+b) for ke N where a and b are fixed for a given case, b varies over the cases and the least significant digit of the integer depends on only b. Note: the least significant digit of an integer is the digit farthest to the right in a integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respec- tively.
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
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,