Determine the possibilities for the final digit of a sixth power of an integer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
6
Transcribed Image Text:1. Only one prime of the form 1+4n exists. Determine this prime number and prove it's the only one of
this particular form. Hint: Research Sophie Germain's Identity to factor 1+4n4.
ad bowollal
ng
(0 be) +
2. Let p be a prime number such that p> 5. Prove that p2 -1 = 0 (mod 24).
odo eit l
3. Let q be a prime and n EN such that 1<n<q. Prove that q
cheofla edt ml
o bo
4. Use the theory of congruences to verify that
25| (27+4 +33n+2 – 53n+6) for all n eN
5. Using congruence theory (not brute force), find all solutions to the following linear congruence:
8x + 9y = 10 (mod 11)
at uq n odT teeW tuo msd hio g ao clett a bodder eio I
Sol ar nd blon sond U
sto bas ,
at bx b ed .
blog sr etth
bing ls
d a
adpah o i obloeb
6. Determine the possibilities for the final digit of a sixth power of an integer.
d to pahvol
bio a (od) eg ) S
y be h
7. Prove that if n is an odd positive integer or divisible by 4, then
13 + 23 + 33 + .. + (n – 1)3 = 0 (mod n)
Is the statement true if n is even but not divisible by 4?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
