PLEASE EXPLAIN AND SHOW WORK STEP BY STEP Use Theorem 6 to compute the least com

Question

PLEASE EXPLAIN AND SHOW WORK STEP BY STEP

Use Theorem 6 to compute the least common multiple of 58 and 124 If f is the mod-5 function, compute each of the following: f(13) + f(19) f(13+19) f(278) Use Bacon's code to create a dummy message for ABANDON. For the sake of simplicity, use bold font for 0 and regular font for 1. Find the greatest common divisor d of the integers 58 and 124, and write d as s(58) + t(124). Write out all of the steps. The following function written in pseudocode accepts INCOME as a variable and outputs the TAX corresponding to that income. What would the pseudocode output with an input of; 23000? 64000? 47000?

Explanation / Answer

1.)Theorem 6: GCD * LCM = product of the two numbers

=> LCM = product of the two numbers / GCD of the two numbers

LCM(58,124) = 58*124 / GCD(58,124)

GCD(58,124)=2

LCM(58,124) = 58*124 / 2

=3596

2.) a.) f(13)+f(19) =  f(2*5 + 3)+f(3*5 + 4) = 3 + 4 = 7

b.) f(13 + 19) = f(32) = f(6*5 + 2) = 2

c.) f(278) = f(55*5 + 3) = 3

3.) Let A = 0 and B = 1

Bacon's code is "Each character from the plaintext is encoded by a word composed of 5 characters. This word only contains the characters A and B"

Sample table for using bacon's code:

Encoding of ABANDON = AAAAA AAAAB AAAAA ABBAA AAABB ABBAB ABBAA

=AAAAAAAAABAAAAAABBAAAAABBABBABABBAA

4.) 124 = 2*58 + 8

58 = 7*8 + 2

8 = 4*2 + 0

Hence 2 is gcd of 58,124

2 = 58 - 7*8

8 = 124 - 2*58

=> 2 = 58 -7(124 - 2*58)

2 = 58 - 7*124 + 14*58

2 = 15*58 - 7*124

4.) a.) TAXDUE = INCOME * 0.08 = 1840 (else condition satisfied)

b.) TAXDUE = 15000 (1st if condition satisfied)

c.) TAXDUE = 5000 (2nd if condition satisfied)

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