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

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

Show that every positive even integer is of the form 2q, for some integer q.

Every prime number greater than 3 is of the fom 6k + 1 or 6k + 5 , where k is some integer.

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

For some integer q, every odd integer is of the form

Find out the sum of the coefficients in the expansion of the binomial (5p - 4q)^n , where n is a +ive integer.

Look at several examples of rational numbers in the form P/q(q ne 0) , where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy ?

Look at several examples of rational numbers in the form P/q(q ne 0) , where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy ?