Home
Class 10
MATHS
Show that the cube of a positive integer...

Show that the cube of a positive integer of the form `6q+r,q` is an integer and r=0,1,2,3,4,5 is also of the form 6m+r

Text Solution

AI Generated Solution

To show that the cube of a positive integer of the form \( n = 6q + r \) (where \( q \) is an integer and \( r = 0, 1, 2, 3, 4, 5 \)) is also of the form \( 6m + r \) for some integer \( m \), we will follow these steps: ### Step 1: Define the number Let \( n = 6q + r \), where \( q \) is an integer and \( r \) can take values \( 0, 1, 2, 3, 4, 5 \). ### Step 2: Cube the number We need to find \( n^3 \): \[ ...
Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYPE QUESTIONS|14 Videos

  • QUADRIATIC EQUATIONS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE|12 Videos

  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ASWERS QUESTIONS|14 Videos

Similar Questions

Explore conceptually related problems

Show that the square of an odd positive integer is of the form 8q+1, for some integer qdot

Show that the square of an odd positive integer is of the form 8q+1, for some integer qdot

Show that the square of any positive integer is of the form 3m or, 3m+1 for some integer m .

Prove that the square of any positive integer of the form 5q+1 is of the same form.

Prove that the square of any positive integer is of the form 4q or 4q+1 for some integer q .

Prove that the square of any positive integer is of the form 4q or 4q+1 for some integer q .

Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.

Show that any positive integer is of the form 3q or, 3q+1 or, 3q+2 for some integer q .

Show that the square of any positive integer cannot be of the form 5q+2 or 5q+3 for some integer q.

Prove that the square of any positive integer is of the form 5q ,5q+1,5q+4 for some integer q.