22. Suppose c is an integer. If c mod 15 = 3, what is10c mod 15? In other words, if division of c by 15 gives aremainder of 3, what is the remainder when 10c is divided%3Dby 15?

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Answered: 22. Suppose c is an integer. If c mod…

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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Question 3 Which of the following is the least common multiple (LCM) of 2-3²-13² and 2-3³7 02⁰.3³ 24-35-13² 2-3-13² 02-3 02¹-3²-132
1. Consider a 4 digit number abcd and show that abcd−(a+b+c+d) is alwaysdivisible by 9. (Ex 1234 − 10 = 1224 = 9 · 136). 2. (A) How many different three-letter initials can a person have?(B) What if the initials are not repeated?(C) What if only consecutive initials are not repeated? ( please just answer part c on this one.. A and B are just so you know the entire question)
(a) At a glance, determine the digit d so that 64,275,67d is divisible by 4. Is there more than one answer? (b) Can you choose the digit d so that 64,275,67d is divisible by 8 and not 16? O A. The digit d can be 6. Oc. The digit d can be 4 or 8. B. The digit d can be 0, 2, or 6. D. The digit d can be 8. O E. The digit d can be 2 or 6. OF. The digit d can be 0. O G. The digit d can be 2. O H. The digit d can be 4. O 1. The digit d can be 0, 2, 4, 6, or 8. O J. The digit d can be 0, 4, or 8.
5. Look at some decimal expressions of fractions such as 325' 5' 15' 20' 14' 50 1 7 9 16 71 50 91 by carrying out long divisions or using your calculator (Careful, calculators can give mis- leading results!), and see which numbers have a terminating decimal expression, while paying attention to the prime factorisation of the denominator. Hint: Take a terminating decimal expression and see what happens when you convert it to a fraction in lowest terms. (Don't include this part in your homework submission.) Now come up with a conjecture for which fractions have a terminating decimal expres- sion. Your conjecture should be of the following form: Let a, b EN with b > 1 and with gcd(a, b) = 1. Then a has a terminating decimal expression iff .... Now prove your conjecture. Note that this is an “if and only if” statement, requiring proofs for both implications.
How would you find -88 mod 13? Please break this down in steps. This one is hard for me.
Solve the following integer

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22. Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c by 15 gives a remainder of 3, what is the remainder when 10c is divided %3D by 15?