11. (a) [Sharescreen]/[Verbal] Write the following statement using mod notation: the last digit of n5 is the same as the last digit of n. (b) [Sharescreen] [Verbal] Hypothesize a mathematical theorem based on the answer from this problem and the previous two. Hint: As long as n is less than the respective mod, n21 (mod 33) = n n25 (mod 35) = n n25 (mod 39) = n n33 (mod 51) = n n³1 (mod 62) = n n61 (mod 77) = n n65 (mod 85) = n n73 (mod 91) = n n61 (mod 93) = n n? (mod ?) = n
11. (a) [Sharescreen]/[Verbal] Write the following statement using mod notation: the last digit of n5 is the same as the last digit of n. (b) [Sharescreen] [Verbal] Hypothesize a mathematical theorem based on the answer from this problem and the previous two. Hint: As long as n is less than the respective mod, n21 (mod 33) = n n25 (mod 35) = n n25 (mod 39) = n n33 (mod 51) = n n³1 (mod 62) = n n61 (mod 77) = n n65 (mod 85) = n n73 (mod 91) = n n61 (mod 93) = n n? (mod ?) = n
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![11. (a) [Sharescreen]/[Verbal] Write the following statement using mod notation: the
last digit of n³ is the same as the last digit of n.
(b) [Sharescreen] / [Verbal] Hypothesize a mathematical theorem based on the answer
from this problem and the previous two.
Hint: As long as n is less than the respective mod,
21
n²¹ (mod 33) = n
n25 (mod 35) = n
n25 (mod 39) = n
n33 (mod 51) = n
n³1 (mod 62) = n
n61 (mod 77) = n
n65 (mod 85) = n
n73 (mod 91) = n
n61
(mod 93) = n
n? (mod ?) = n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff97c0725-689e-40d7-87a0-46553d65cfc3%2F67166768-b46e-438d-9e7a-335828d6a6a8%2Fqpcu2g7_processed.png&w=3840&q=75)
Transcribed Image Text:11. (a) [Sharescreen]/[Verbal] Write the following statement using mod notation: the
last digit of n³ is the same as the last digit of n.
(b) [Sharescreen] / [Verbal] Hypothesize a mathematical theorem based on the answer
from this problem and the previous two.
Hint: As long as n is less than the respective mod,
21
n²¹ (mod 33) = n
n25 (mod 35) = n
n25 (mod 39) = n
n33 (mod 51) = n
n³1 (mod 62) = n
n61 (mod 77) = n
n65 (mod 85) = n
n73 (mod 91) = n
n61
(mod 93) = n
n? (mod ?) = n
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