Home
Class 10
MATHS
By Euclid's division lemma, show that th...

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.

Text Solution

Verified by Experts

The correct Answer is:
3M+2
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • REAL NUMBERS

    OSWAAL PUBLICATION|Exercise TOPIC -1 EUCLID.S DIVISION ALGORITHM ( LONG ANSWER TYPE QUESTIONS -1)|4 Videos

  • REAL NUMBERS

    OSWAAL PUBLICATION|Exercise TOPIC -1 EUCLID.S DIVISION ALGORITHM ( LONG ANSWER TYPE QUESTIONS -II)|2 Videos

  • REAL NUMBERS

    OSWAAL PUBLICATION|Exercise TOPIC -1 EUCLID.S DIVISION ALGORITHM ( VERY SHORT ANSWER TYPE QUESTIONS )|9 Videos

  • QUADRATIC EQUATIONS

    OSWAAL PUBLICATION|Exercise TEXTBOOK CORNER (EXERCISE 10.4) |8 Videos

  • SOLVED PAPER (SSLC KARNATAKA APRIL 2019)

    OSWAAL PUBLICATION|Exercise Answer the following :|29 Videos

Similar Questions

Explore conceptually related problems

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 .]

Use Euclid's division lemma lo show that the square of any positive integer is either of th.e 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 division algorithm to show that the square of any positive integer is of the form 3p or 3p + 1.

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

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 cube of any positive integer is of the form 9 m, 9m + 1 or 9m + 8.

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

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

Home
Profile