Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Grace remembers that if they wanted to buy some number of $91 items, spending 77 times the amount of money Owed would return $14 in change. That is, 77x 14 (mod 91). Leah remembers that if they wanted to buy some number of $28 items, spending 12 times the amount of money wed would return $8 in change. That is, 12x 8 (mod 28). a) Find a single value of a that solves both congruences. b) Grace says, "I found a value of that solves both congruences, but it took a stupendously long time using trial ar error." Leah gloats, "I was able to find a value of a without using any trial and error!" Briefly describe how Leah might have found their answer to part (a)

Grace remembers that if they wanted to buy some number of $91 items, spending 77 times the amount of money Owed would return $14 in change. That is, 77x 14 (mod 91). Leah remembers that if they wanted to buy some number of $28 items, spending 12 times the amount of money wed would return $8 in change. That is, 12x 8 (mod 28). a) Find a single value of a that solves both congruences. b) Grace says, "I found a value of that solves both congruences, but it took a stupendously long time using trial ar error." Leah gloats, "I was able to find a value of a without using any trial and error!" Briefly describe how Leah might have found their answer to part (a)

Advanced Engineering Mathematics
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
icon
Related questions
Question
(c) Suppose x and y are both solutions to the pair of congruences. What is the smallest possible positive value of x - y? (d) Briefly explain your answer to part (c).
Transcribed Image Text:(c) Suppose x and y are both solutions to the pair of congruences. What is the smallest possible positive value of x - y? (d) Briefly explain your answer to part (c).
Grace owes Leah some money, but neither of them can remember how much! Let $x be the amount of money owed, where x is some positive integer. Grace remembers that if they wanted to buy some number of $91 items, spending 77 times the amount of money owed would return $14 in change. That is, 77x 14 (mod 91). Leah remembers that if they wanted to buy some number of $28 items, spending 12 times the amount of money owed would return $8 in change. That is, 12x = 8 (mod 28). (a) Find a single value of that solves both congruences. (b) Grace says, "I found a value of a that solves both congruences, but it took a stupendously long time using trial and error." Leah gloats, "I was able to find a value of x without using any trial and error!" Briefly describe how Leah might have found their answer to part (a).
Transcribed Image Text:Grace owes Leah some money, but neither of them can remember how much! Let $x be the amount of money owed, where x is some positive integer. Grace remembers that if they wanted to buy some number of $91 items, spending 77 times the amount of money owed would return $14 in change. That is, 77x 14 (mod 91). Leah remembers that if they wanted to buy some number of $28 items, spending 12 times the amount of money owed would return $8 in change. That is, 12x = 8 (mod 28). (a) Find a single value of that solves both congruences. (b) Grace says, "I found a value of a that solves both congruences, but it took a stupendously long time using trial and error." Leah gloats, "I was able to find a value of x without using any trial and error!" Briefly describe how Leah might have found their answer to part (a).
Expert Solution
steps

Step by step

Solved in 3 steps with 8 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS