Discrete Mathematics for Computer Scientists -- Assignment 5 - ArithmeticDIT980, HT 2015
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Assignment Week 5 - Arithmetic

Please submit using the Fire system


(1.) Consider the following two diophantine equations. For each one, explain whether or not it has a solution. If there are any solutions, give three different solutions.

(a) 17x + 22y = 6

(b) 22x - 55y = 13

(2.) Consider the following three congruences:

x ≡ 1 (mod 3)

x ≡ 2 (mod 5)

x ≡ 3 (mod 7)

(a) Find an integer x that satisfies all three congruences simultaneously. Use the Chinese Remainder Theorem, and explain how you reached your solution, step by step.

(b) What solutions are there such that 0 ≤ x ≤ 200?

(3.) Show that for all integer numbers x, it is never the case that x2 ≡ 2 (mod 3).

Hint: Consider the remainder ("rest") when dividing x by 3.


Submission of this assignment should be done electronically through the Fire system.

The submission deadline is Wednesday, October 7, at 13:00. At this time, you should have submitted a serious attempt to solve the assignment. A serious attempt is either an answer you believe to be correct, or a partial answer plus a detailed explanation of what you have tried to come up with a full answer. An empty document is not a serious attempt.

After submitting, you have until October 19 (midnight) to submit a completely correct version.

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