The following is a list of converse statement of modular arithmetic. Determine if any of the followingresults hold true.ACTIVITIES AND ASSIGNMENTS FOR WEEK 23(0) If a x k = b x k mod n for any integer k, then (r) If a = b' mod n for any positive integer l, thena = b mod n.(p) If a² = b² mod n, then a = b mod n.(g) If a³ = b³ mod n, then a = b mod n.a = b mod n.(s) If 2ª = 2º mod n, then a = b mod n.(t) If 3ª = 3º mod n, then a = b mod n.3Again, remember that the above list from (a) to (t) are not all true. Some of them are false. Pick yourfavorite fact and do the followings: (1) First pick different values of a, b, n (or k, or l if they appear) to test the fact. Ideally your valuesshould involve a variety of numbers (positive, negative, zero, large, small).(2) Second determine whether it is true or false.(3) Then try give a justification (preferably a mathematical proof like above) of your claim that youthink will convince your most hardened skeptical classmates.(4) You also need to respond to two other students' threads, contributing your questions, observations,and thoughts on their explanations.

Since you have asked multiple question, we will solve the first question for you. If you want any…

The following is a list of converse statement of modular arithmetic. Determine if any of the following results hold true. ACTIVITIES AND ASSIGNMENTS FOR WEEK 2 3 (0) If a × k = b x k mod n for any integer k, then a = b mod n. (p) If a² = b² mod n, then a = b mod n. (g) If a³ = b³ mod n, then a = b mod n. (r) If aº = b' mod n for any positive integer l, then a = b mod n. (s) If 2ª = 26 mod n, then a = b mod n. (t) If 3ª = 36 mod n, then a = b mod n. Again, remember that the above list from (a) to (t) are not all true. Some of them are false. Pick your favorite fact and do the followings:

The following is a list of converse statement of modular arithmetic. Determine if any of the following results hold true. ACTIVITIES AND ASSIGNMENTS FOR WEEK 2 3 (0) If a × k = b x k mod n for any integer k, then a = b mod n. (p) If a² = b² mod n, then a = b mod n. (g) If a³ = b³ mod n, then a = b mod n. (r) If aº = b' mod n for any positive integer l, then a = b mod n. (s) If 2ª = 26 mod n, then a = b mod n. (t) If 3ª = 36 mod n, then a = b mod n. Again, remember that the above list from (a) to (t) are not all true. Some of them are false. Pick your favorite fact and do the followings:

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

The following is a list of converse statement of modular arithmetic. Determine if any of the following
results hold true.
ACTIVITIES AND ASSIGNMENTS FOR WEEK 2
3
(0) If a x k = b x k mod n for any integer k, then (r) If a = b' mod n for any positive integer l, then
a = b mod n.
(p) If a² = b² mod n, then a = b mod n.
(g) If a³ = b³ mod n, then a = b mod n.
a = b mod n.
(s) If 2ª = 2º mod n, then a = b mod n.
(t) If 3ª = 3º mod n, then a = b mod n.
3
Again, remember that the above list from (a) to (t) are not all true. Some of them are false. Pick your
favorite fact and do the followings:

(1) First pick different values of a, b, n (or k, or l if they appear) to test the fact. Ideally your values
should involve a variety of numbers (positive, negative, zero, large, small).
(2) Second determine whether it is true or false.
(3) Then try give a justification (preferably a mathematical proof like above) of your claim that you
think will convince your most hardened skeptical classmates.
(4) You also need to respond to two other students' threads, contributing your questions, observations,
and thoughts on their explanations.

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