The set of intergers can be classified into k classes, according to the remainder obtained when they are divided by K (where is a fixed natural number). The classification enables is solving even some more difficult problems of number theory e.g.
(i) even, odd classification is based on whether ramainder is 0 or 1 when divided by 2.
(ii) when divided by 3, the ramainder may be 0,1,2. Thus, there are three classes.
The number obtained, when the square of an integer is divided by 3, is

Options

A. (a)2
B. (b)3
C. (c)1
D. (d)None of these

Answer

To solve the problem of finding the possible remainders when the square of an integer is divided by 3, we can follow these steps:

### Step 1: Identify the forms of integers
We can express any integer \( n \) in terms of its remainder when divided by 3. The possible forms of integers are:
- \( n = 3k \) (where the remainder is 0)
- \( n = 3k + 1 \) (where the remainder is 1)
- \( n = 3k + 2 \) (where the remainder is 2)