Home
Class 12
MATHS
Prove that 13^99-19^93 is divisible by 1...

Prove that `13^99-19^93` is divisible by 162.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Binomial Theorem for Positive Integrel Index

    A DAS GUPTA|Exercise Exercise|113 Videos

  • Application of dy/dx

    A DAS GUPTA|Exercise Exercise|45 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

Similar Questions

Explore conceptually related problems

(2^19+1) is divisible by :

19^(5)+21^(5) is divisible by

Prove that 33! Is divisible by 2^(19) and what is the largest integer n such that 33! Is divisible by 2^(n) ?

(2^(19) + 1) is divisible by :

Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove that a+d is divisible by 13.

Check whether 377910 is divisible by 13.

Find out whether 21793 is divisible by 19.

If 13^99-19^93 is divided by 162, then the remainder is

Using the sum of G.P., prove that a^(n)+b^(n)(a,binN) is divisble by a+b for odd natural numbers n. Hence prove that 1^(99)+2^(99)+….100^(99) is divisble by 10100

Check whether 2366 is divisible by 13.

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Prove that 13^99-19^93 is divisible by 162.

    Text Solution

    |

  2. Determine the constant term in the expansion of (1+x+x^2+x^3)^10

    Text Solution

    |

  3. If the fourth term in the expansion of (px+1/x)^n is 5/2, then (n,p)...

    Text Solution

    |

  4. Show that there wil be a term independent of x in the expansion of (x^...

    Text Solution

    |

  5. Find the term which does not contain irrational expression in the expa...

    Text Solution

    |

  6. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

    Text Solution

    |

  7. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

    Text Solution

    |

  8. Prove that the coefficient of the middle term in the expansion of (1+x...

    Text Solution

    |

  9. In the expansion of (1 + x)^43 ,the co-efficients of (2r + 1)th and (r...

    Text Solution

    |

  10. Prove that in the expansion of (1+x)^(2n), the coefficient of x^n is d...

    Text Solution

    |

  11. The coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n ...

    Text Solution

    |

  12. Given positive integers r>1,n> 2, n being even and the coefficient of...

    Text Solution

    |

  13. If the coefficients of three consecutive terms in the expansion of (1 ...

    Text Solution

    |

  14. If a,b,c be the three consecutive coefficients in the expansion of a p...

    Text Solution

    |

  15. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  16. If a,b,c and d are any four consecutive coefficients in the expansi...

    Text Solution

    |

  17. If the four consecutive coefficients in any binomial expansion be a, b...

    Text Solution

    |

  18. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

    Text Solution

    |

  19. If n be a positive integer then prove that the integral part P of (5+2...

    Text Solution

    |

  20. If (9+4sqrt5)^n=p+beta where n and p are positive integers and beta is...

    Text Solution

    |

  21. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

    Text Solution

    |