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

An assignment is posted on Monday at 6 AM and is due in 155 hours. Determine the exact day and time of the deadline.

(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 :