Quiz (Divisibility)

(1) Find the number of positive integers not exceeding 1000 that are divisible by 3 but not by 4.

(2) Use mathematical induction to show that is divisible by 5 for every positive integer

(3) Show that any integer of the form is also of the form but not conversely.

(4) Use the Division Algorithm to show that the square of any integer is either of the form or

(5) Use the Division Algorithm to show that the cube of any integer has one of the forms or

(6) Use the Division Algorithm to show that the fourth power of any integer is either of the form or

(7) Show that the cube of any integer is of the form or

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