A. Observe that 15 = 1 ??? 715^2 = 225 ???7 = 1 ??? 715^3 = 3375 ???7 = 1 ??? 7Can you see a pattern? Using what you’ve learned from above, what is 15^289 ??? 7?B. Suppose ? = 5⨀? ۩ 3 in ?6. Solve for x. Examples:4 @ 5 — 9 тod7 — 2 тod75 03 — 8 тod7 — 1 mod7ЗО3%3D 9 тоd7 — 2 тod76043 24 тod6 — 3 тod7e 012 3 4 5 600 12 3 4 5 61 1 2 3 4 5 6 02 2 3 45 6 0 13 3 4 5 6 0 1 24 4 5 6 0 12 35 5 601 2 3 46 6 012 3 4 5O 01 2|3 4 5 6In Z, , the additive inverses are0 00000 0 01012 3 4 5 62 0 2 46 13 53 036 2 5 1 44 04 15 2 6 35 053 16 4 26 06 5 4 3 2 11245Inv54321Since 7 is prime , all nonzero elements havemult. inverse101 = 1 mod72 O 4 = 1 mod7305%3D 1 тоd74 © 2 = 1 mod75 0 3 = 1 mod7606=1 mod7Addition and Multiplication in Z,12346Mult46.Inv Examples:3Ө5 3 8 тod6 — 2 тod62 0 4 = 6 mod6 = 0 mod64 0 3 = 7 mod6 = 1 mod62 О33D 6тod6 — 0 тod64 05 %3D 20 тod6 — 2 тоd6ReviewO0 12 300 0000 010 12 3 4 52 0 240 2 43 03O 012 34 500 12 3 4 51 1 2 3 4 5 02 2 3 45 0 13 34 5 01 24 45 01 2 35 5 01In Z6 , the additive inverses are2453 0 3 04 04 2 0 4 25 0 5 4 3 2Inv.412 3 41Since 6 is not prime andk12345Gcd(k,6)11Addition and Multiplication in Z6Only 1 and 5 have multiplicative inverse1013D1 тod65 05%3 1 тоd6k15| Inv.(reciprocal)1

This is a problem of modular arithmetic, congruence, number theory, abstract Algebra.

A. Observe that 15 = 1 ??? 7 15^2 = 225 ???7 = 1 ??? 7 15^3 = 3375 ???7 = 1 ??? 7 Can you see a pattern? Using what you’ve learned from above, what is 15^289 ??? 7? B. Suppose ? = 5⨀? ۩ 3 in ?6. Solve for x.

A. Observe that 15 = 1 ??? 7 15^2 = 225 ???7 = 1 ??? 7 15^3 = 3375 ???7 = 1 ??? 7 Can you see a pattern? Using what you’ve learned from above, what is 15^289 ??? 7? B. Suppose ? = 5⨀? ۩ 3 in ?6. Solve for x.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

0.041 in scientific notation?
What is 5/6 x 2/4
2. to model the number of picograms of carbon-14 5,730 A scientist uses the expression (2.5)•G) 3:740 remaining in a different fossil t years after 20,000 BC. a. What do the 2.5, , and 5,730 mean in this situation? 2 b. Would more or less than .1 picogram of carbon-14 remain in this fossil today? Explain how you know.
Ee.4.
Find ∑x. Find ∑x. X 0.001 0.029 0.136 0.259 0.470 enter your response here ∑x= (Type an integer or a decimal. Do not round.)
QUESTION 14 Use the diagram below to explaing why 1 %3D DEand ther the file You will need to write or draw diag 寸|5