MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
Consider any integer n.
(i) When n is divided by 3, list all possible remainders and write n in an algebraic form for each case.
(ii) Show that the square of any integer is either of the form 3k or 3k+1, where k is an integer.
(iii) Hence, explain why no perfect square can give a remainder of 2 when divided by 3.