MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
Answer the following:
(i) When any integer is divided by 2, what possible remainders can it leave? Write the integer in an algebraic form for each case.
(ii) Hence, show that every odd integer can be written in the form 2k+1 or 2k−1, where k is an integer.
(iii) Using the result of part (ii), explain why the product of two odd integers is always odd.