Home
Class 12
MATHS
Find the largest positive integer n such...

Find the largest positive integer n such that `2^(n)` divides `3^(4096)-1`

Text Solution

Verified by Experts

The correct Answer is:
14
Promotional Banner

Topper's Solved these Questions

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos
  • COMBINATORICS

    RESONANCE|Exercise Exercise-1 (Part-II RMO)|17 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise High Level Problems (HLP)|33 Videos
  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

Similar Questions

Explore conceptually related problems

Find the least positive integer n such that ((2i)/(1+i))^(n) is a positive integer.

If n is the largest positive integer such that 33! is divisible by 2^(n) , then value of n-30 is.

The least positive integer n such that 2 divides n,3 divides n+1,4 divides n+2,5 divides n+3 and 6 divides n+4 is

Compute the largest positive integer,n,such that ((2007)!)/((2007)^(n)) is an integer.

The largest integer lambda such that 2^(lambda) divides 3^(2^(n))-1, ninN is

RESONANCE-COMBINATORICS-Exercise-2 (Part-I: Previous Asked Question for Pre RMO)
  1. Consider all the 7-digit numbers containing each of the digits 1,2,3,4...

    Text Solution

    |

  2. Determine the largest 2-digit prime factor of the integer ((200),(100)...

    Text Solution

    |

  3. Find the sum of all the distinct prime divisors of underset(r=0)overse...

    Text Solution

    |

  4. Let n!, the factorial of a positive integer n, be defined as the produ...

    Text Solution

    |

  5. Find the number of ordered pairs of positive integers (a,b) such that ...

    Text Solution

    |

  6. Find the largest positive integer n such that 2^(n) divides 3^(4096)-1

    Text Solution

    |

  7. The total number of possible line segments having both end points loca...

    Text Solution

    |

  8. At a couple dance party, each man danced with exactly four women and e...

    Text Solution

    |

  9. On a stormy night ten guests came to dinner party and left their shoes...

    Text Solution

    |

  10. There are three kinds of fruits in the market. How many ways are there...

    Text Solution

    |

  11. Find the coefficient of a^(5) b^(5)c^(5)d^(8) in the expansion of the ...

    Text Solution

    |

  12. Find the total number of times the digit '2' appears in the set of int...

    Text Solution

    |

  13. Find the number of pairs of positive integers (m,n) with m le n, such ...

    Text Solution

    |

  14. How many positive integers less than 1000 have the property that the s...

    Text Solution

    |

  15. There are five cities A, B, C, D, E on a certain island. Each city is ...

    Text Solution

    |

  16. There are eight rooms on the first floor of a hotel, with four rooms o...

    Text Solution

    |

  17. Find the number of ordered triples (a,b,c) of positive integers such t...

    Text Solution

    |

  18. Suppose in the plane 10 pair wise non parallel lines intersect one ano...

    Text Solution

    |

  19. There are several tea cups in the kitchen, some with handle and the ot...

    Text Solution

    |

  20. Determine the number of 8-tuples (in(1), in(2),…, in(8)) such that in(...

    Text Solution

    |