Home
Class 10
MATHS
Use Euclid's division lemma to show that...

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

Promotional Banner

Topper's Solved these Questions

  • REAL NUMBERS

    R G PUBLICATION|Exercise EXERCISE|84 Videos

  • QUADRATIC EQUATIONS

    R G PUBLICATION|Exercise EXERCISE|115 Videos

  • REVISION

    R G PUBLICATION|Exercise EXERCISE|243 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.

Show that cube of any positive integer is either of the form 4q, 4q+1, 4q+3 for (q in Z)

Show that any positive even integer is of the form 6q, 6q+2 ,6q+4.

Euclid's division Lemma states that if a and b are any two positive integers,then there exists unique integers q and r such that

For some positive integer m,every positive even integer is of the form a)m-1 b)m+1 c)2m d)2m+1

Show that 0.bar9 = 1

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

For which of these would you use a histogram to show the data? The number of passengers boarding trains form 7.00 a.m. to 7.00 p.m at a station. Give reasons for each.

Every even integer is of the form 2m,where m is an integer.True or False

If q is a positive integer, square of every integer can be expressed in the form of 8q+1.

R G PUBLICATION-REAL NUMBERS-EXERCISE
  1. An army contingent of 616 members is to march behind an army band of 3...

    Text Solution

    |

  2. Use Euclid's division lemma to show that the square of any positive in...

    Text Solution

    |

  3. Use Euclid's division lemma to show that the cube of any positive inte...

    Text Solution

    |

  4. Express each number as a product of its prime factors:(i)140

    Text Solution

    |

  5. Express each number as a product of its prime factors:(ii) 156

    Text Solution

    |

  6. Express each number as a product of its prime factors:(iii)3825

    Text Solution

    |

  7. Express each number as a product of its prime factors:(iv)5005

    Text Solution

    |

  8. Express each number as a product of its prime factors:(v)7429

    Text Solution

    |

  9. Find the LCM and HCF of the following pairs of integer and verify that...

    Text Solution

    |

  10. Find the LCM and HCF of the following pairs of integer and verify that...

    Text Solution

    |

  11. Find the LCM and HCF of the following pairs of integer and verify that...

    Text Solution

    |

  12. Find the LCM and HCF of the following integers by applying the prime f...

    Text Solution

    |

  13. Find the LCM and HCF of the following integers by applying the prime f...

    Text Solution

    |

  14. Find the LCM and HCF of the following integers by applying the prime f...

    Text Solution

    |

  15. Given that HCF (306,657)=9,find LCM (306,657)

    Text Solution

    |

  16. Check whether 6^n can end with the digit 0 for any natural number n.

    Text Solution

    |

  17. Explain why 7xx11xx13+13 and 7xx6xx5xx4xx3xx2xx1+5 are composite numbe...

    Text Solution

    |

  18. There is a circular path around a sports field.Sonia takes 18 minutes ...

    Text Solution

    |

  19. Prove that sqrt5 is irrational.

    Text Solution

    |

  20. Prove that 3+2sqrt5 is irrational.

    Text Solution

    |