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

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.

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

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

Write down the form of any square of an positive integer.

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

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

For some positive integer n,every positive odd integer is of the form

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

Write down the form of any positive integer: When it is dividing by 3.

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

Write down the form of any positive integer: When it is dividing by 2.

R G PUBLICATION-REAL NUMBERS-EXERCISE
  1. Show that any positive odd interger is of the form 6q+1,or 6q+3,or 6q+...

    Text Solution

    |

  2. An army contingent of 616 members is to march behind an army band of 3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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 pairs of integer and verify that...

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Prove that sqrt5 is irrational.

    Text Solution

    |