Use division algorithm to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer

Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is some integer.

Use division algorithm to show that the cube of any positive integer is of the form 9 m, 9m + 1 or 9m + 8.

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

The square of an odd integer is of the form 4q + r where r is :

Show that the square of any positive integer of the form 3m or 3m + 1 for some integer n.

Show that one and only one out of n, n + 2 or n + 4 is divisible by 3, where n is any positive integer

Find the sum ofthe first 40 positive integers divisible by 6.

Find the least positive integer n such that 1 + 6 +6^2 + … + 6^n gt 5000

Euclid's division lemma states that for positive integers a and b, there exist unique integers q and r such that a=bq+r , where r must satisfy.