Home
Class 10
MATHS
Show that the square of any odd integer ...

Show that the square of any odd integer is of the form 4q +1 for any integer q.

Text Solution

Verified by Experts

The correct Answer is:
4q+1
Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    ZEN PUBLICATION|Exercise ADDITIONAL QUESTIONS(SHORT ANSWER TYPE 2 QUESTIONS)|7 Videos

  • QUADRATIC EQUATIONS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS (IIT FOUNDATION)|5 Videos

  • SOME APPLICATIONS OF TRIGONOMETRY

    ZEN PUBLICATION|Exercise ADDITIONAL QUESTIONS (VALUE BASED QUESTIONS )|2 Videos

Similar Questions

Explore conceptually related problems

Show that square of any odd integer is of the form 4q + 1 for some integer q.

Show that the square of any positive odd integer is of the form 4q + 1 for any integer q.

Use division algorithm to show that the square of any positive integer is of the form 3p or 3p + 1.

Prove that the square of any positive integer of the form 5q +1 will be in the same form.

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square each of these and show that they can be rewritten in the form 3m or 3m+1].

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m . (Hint : Let x be any positive integer then it is of the form 3q , 3q +1 or 3q + 2 . Now square each of these and show that they can be rewritten in the form 3m or 3m + 1 .]

By Euclid's division lemma, show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.

Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m , 9m +1 or 9m + 8 .

Use division algorithm to show that the cube of any positive integer is of the form 9 m, 9m + 1 or 9m + 8.