In this exercise set, all variables are integers.1. List the distinct congruence classes modulo 5, exhibiting at least three elements ineach class.2. Follow the instructions in Exercise 1 for the congruence classes modulo 6. 20. 79x = 83 (mod 61)

We can solve this using linear congruence method

Answered: In this exercise set, all variables are…

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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hello by Peter Linz, "Introduction to Formal Languages and Automaton", 6th edition, 2017. The cut is from chapter 2, section 1. thanks:))
94 is congruent to modulo 15. (Find an integer n that is satisfies 0 ≤ n < 15.)
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Squares are controlled modulo 16. Preamble. Recall the equivalence class, [al, of an integer, a, modulo an integer, b, is the set of all integers c satisfying: ca (modulo b), read "c is equivalent to a modulo b", i.e. blc-a, read "b divides c-a", i.e. there exists an integer n satisfying: bn=c-a, (1) (3) read "c-a is divisible by b", e.g. the equivalence class, [3], of 3 modulo 16 is the set of all integers c which are equivalent to 3 modulo 16, i.e. the set (2) ...,-13, 3, 19, 35, .... {ee Z such that there exists an integer n satisfying 16n-c-3, i.e. c=16n+3}. Intuitively, these are integers whose remainder is 3 upon division by 16, e.g. End preamble. What are the possible equivalence classes of a square medulo 16? Prove your claim.
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In this exercise set, all variables are integers. 1. List the distinct congruence classes modulo 5, exhibiting at least three elements in each class. 2. Follow the instructions in Exercise 1 for the congruence classes modulo 6.