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

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

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

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.

Using Euclid's division lemma, if the cube of any positive integers is divided by 9 then the possible remainders are ___.

An arc of a bridge is semi-elliptical with the major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then prove that the best approximation of the height of the acr 2 m from the center of the base is 8/3mdot

Use the Principle of Mathematical Induction to verify that, for n any positive integer, 6 ^n −1 is divisible by 5 .

The number of ordered pairs of positive integers (m,n) satisfying m le 2n le 60 , n le 2m le 60 is

Prove the 2^(n)+6times9^(n) is always divisible by 7 for any positive integer n.