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For any positive integer n , prove th...

For any positive integer `n` , prove that `n^3-n` divisible by 6.

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RD SHARMA-REAL NUMBERS-All Questions
  1. Use Euclids division Lemma to show that the cube of any positive in...

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

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  3. For any positive integer n , prove that n^3-n divisible by 6.

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  4. Prove that if a positive integer is of the form 6q+5 , then it is o...

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

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  6. Prove that the square of any positive integer is of the form 4q or ...

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  7. Show that any positive odd integer is of the form 6q+1 or, 6q+3 or,...

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  10. Find the largest number which divides 245 and 1029 leaving remainde...

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  11. In a seminar. the number of participants in Hindi, English and Mathema...

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  12. Define HCF of two positive integers and find the HCF of the followi...

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  13. Define HCF of two positive integers and find the HCF of the followi...

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  14. Define HCF of two positive integers and find the HCF of the followi...

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  15. Define HCF of two positive integers and find the HCF of the followi...

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  16. Use Euclid’s division algorithm to find the HCF of (i) 135 and 225 ...

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  17. Find the HCF of the following pairs of integers and express it as a ...

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  18. Express the HCF of 468 and 222 as 468 x+222 y where x ,\ y are inte...

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  19. If the HCF of 408 and 1032 is expressible in the form 1032\ m-408xx...

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  20. If the HCF of 657 and 963 is expressible in the form 657\ x+963xx-1...

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