Home
Class 10
MATHS
The remainder when the square of any pri...

The remainder when the square of any prime number greater than `3` is divided by `6` is

Text Solution

AI Generated Solution

To find the remainder when the square of any prime number greater than 3 is divided by 6, we can follow these steps: ### Step 1: Identify the form of prime numbers greater than 3 Any prime number greater than 3 can be expressed in one of the following forms: - \(6n - 1\) - \(6n + 1\) where \(n\) is a natural number. ...
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

The remainder obtained when any prime number greater than 6 is divided by 6 must be either 1 or 2 (b) either 1 or 3 either 1 or 5 (d) either 3 or 5

Find the remainder when the square of any number is divided by 4

A prime number greater than 11 will never end with

When the square of any odd number, greater than 1, is divided by 8, it always leaves remainder 1 (b) 6 (c) 8 (d) Cannot be determined

A number when divided by 6leaves remainder 3. When the square of the same number is divided by 6,find the remainder.

If a number is divided by 6, the remainder is 3 then what will be the remainder when the square of the same number is divided by 6 again?

RD SHARMA-REAL NUMBERS-All Questions
  1. Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, whe...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Show that there is no positive integer n for which sqrt(n-1)+sqrt(n+1...

    Text Solution

    |

  16. A merchant has 120 litres of oil of one kind, 180 litres of another ...

    Text Solution

    |

  17. Two brands of chocolates are available in packs of 24 and 15 respec...

    Text Solution

    |

  18. What is the largest number that divides 626, 3127 and 15628 and lea...

    Text Solution

    |

  19. Find the greatest number that will divide 445, 572 and 699 leaving ...

    Text Solution

    |

  20. Two tankers contain 850 litres and 680 litres of petrol respectively. ...

    Text Solution

    |