a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7. b) Write the prime factorization of 229320 and 49140. Hence, find GCD and LCM. c) Convert the following number (8091) 10 to base 2 d) Find

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
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a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7.
b) Write the prime factorization of 229320 and 49140. Hence, find GCD and
LCM.
c) Convert the following number (8091) 10 to base 2.
d) Find al integers a such that a = 3a (mod 7).
e) Use the cipher: f(x) = (x + 10) mod 26,0 ≤ x ≤5 to decrypt "SD SC XYD
PKSB".
Transcribed Image Text:a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7. b) Write the prime factorization of 229320 and 49140. Hence, find GCD and LCM. c) Convert the following number (8091) 10 to base 2. d) Find al integers a such that a = 3a (mod 7). e) Use the cipher: f(x) = (x + 10) mod 26,0 ≤ x ≤5 to decrypt "SD SC XYD PKSB".
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