Question

Prove that every odd positive integer is either of the form 6q+1 or 6q+3 or 6q+4

Answer 1

Given:

• A number in form of

1. 6q+1
2. 6q+3
3. 6q+5

(correct Question).

To Prove :

• Every odd number is in form of 6q+1 ,6q+3 & 6q+5.

Concept Used:

• We will use 'Euclids Division Lemma' to prove the given statement.

Answer:

For answer refer to attachment:

So ,from the above discussion we can say that every odd number is in form of 6q+2 , 6q+3 or 6q + 5 ,where q is some integer.

Extra information:

• Every odd number is also in form of 4q+1 or 4q +3 .
• Cube of every odd positive number is in form of 9m ,9m+1 or 9m +8.

(Here q and m are integers.)

Answer 2

$\huge \: thank \: you$