(1) For any integers  and , if  and , then . True or false?  (2) There exist integers  and  such that , and . True or false?  

(1) There exist integers  and such that  

Let  and  be integers. Is

Let  and be integers. Is true?

An assignment is posted on Monday at 9 AM and is due in 110 hours. Determine the exact day and time of the deadline.

(6 points for the correct answer. Extra 1 bonus point if you have correctly answered 7 questions among questions 1 through 7 and question 9.) Let 

Suppose m and n are integers such that  and .  Then   (Please enter your answer as an integer.)

In this question, we will prove directly the following statement :   

(6 points for the correct answer. Extra 1 bonus point if you have correctly answered 7 questions among questions 1 through 8.) We wish to prove the following statement by mathematical induction:        

This assignment must be submitted by the end of class. Only one assignment will be submitted for each group (the same grade will be given to all those in the group). You are not to use ChatGPT or any similar AI drafting platform for this assignment, but you may use any kind of legal or internet general research sites. Please complete the names of the other students in your group:________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________