Question

show that any positive odd integer is of the form 3m or 3m+1 or 3m +2, where ‘m’ is some integer​

Answer 1

Answer:

case 1 if m is even integer then 3m is even but 3m+1 is odd and 3m+2 is even

case 2 when m is odd integer

the 3m is odd 3m+1 is even and 3m+2 is odd

Answer 2

Step-by-step explanation:

let x be any integer

now when x is divided by 3, there are three possibilities

1. the integer is divisible by 3

i.e. x = 3m

2. the integer is not divisible by 3 and the remainder is 1

i.e. x = 3m +. 1

3. the integer is not divisible by 3 and the remainder is 2.

now x= 3m is even for even m and odd for odd m.

3m+1 is always odd for all m

3m+2 is even for even m and odd for odd m.

thus any integer can be represented by the form mentioned at 1,2 and 3 above so can odd integer be