• 1

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

  • 1

The ncert question of Class 10 Chapter 1 – Real Number Exercise 1.1 . How can i solve this question. I want, simple way for solving this question because it is very important question.


1 Answer

  1. Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

    Now substituting the value of r, we get,

    If r = 0, then a = 6q

    Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

    If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

    • 1
Leave an answer

Leave an answer


Choose from here the video type.

Put Video ID here: Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions