Home
Class 10
MATHS
Prove that one of every three consecutiv...

Prove that one of every three consecutive positive integers is divisible by 3.

Text Solution

Verified by Experts

Let `n,n+1,n+2` be three consecutive positive integers.
we can write,
By Euclid's division lemma
`n=bq+r`
Where` b=3`
...
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    RD SHARMA|Exercise All Questions|390 Videos
  • SOME APPLICATIONS OF TRIGONOMETRY

    RD SHARMA|Exercise All Questions|154 Videos

Similar Questions

Explore conceptually related problems

prove that the product of three consecutive positive integers is divisible by 6.

" The product of three consecutive positive integers is divisible by "

Prove that the product of two consecutive positive integers is divisible by 2 .

Prove that the product of 2n consecutive negative integers is divisible by (2n)!

find three consecutive positive even integers whose sum is 90.

RD SHARMA-REAL NUMBERS-All Questions
  1. Express each of the following positive integers as the product of its ...

    Text Solution

    |

  2. If a and b are two odd positive integers such that a > b, then prove t...

    Text Solution

    |

  3. Prove that one of every three consecutive positive integers is divi...

    Text Solution

    |

  4. Show that the square of an odd positive integer is of the form 8q+1, f...

    Text Solution

    |

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

    Text Solution

    |

  6. Prove that if xa n dy are odd positive integers, then x^2+y^2 is even ...

    Text Solution

    |

  7. Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, whe...

    Text Solution

    |

  8. Prove that n^2-n divisible by 2 for every positive integer n.

    Text Solution

    |

  9. The remainder when the square of any prime number greater than 3 is ...

    Text Solution

    |

  10. Use Euclid’s division algorithm to find the HCF of 4052 and 12576.

    Text Solution

    |

  11. Use Euclid’s division algorithm to find the HCF of 210 and 55.

    Text Solution

    |

  12. If n is a natural number, then 9^(2n)-4^(2n) is always divisible by 5 ...

    Text Solution

    |

  13. What can you say about the prime factorisations of the denominators of...

    Text Solution

    |

  14. If p1a n dp2 are two odd prime numbers such that p1> p2, then p1 2-p2 ...

    Text Solution

    |

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

    Text Solution

    |

  16. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. It is to ...

    Text Solution

    |

  17. If the prime factorization of a natural number n is 2^3*3^2*5^2*6, w...

    Text Solution

    |

  18. A circular field has a circumference of 360km. Three cyclists start ...

    Text Solution

    |

  19. In a morning walk three persons step off together, their steps measure...

    Text Solution

    |

  20. Prove that sqrt(2)+sqrt(5) is irrational.

    Text Solution

    |