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Prove that a positive integer n is prime...

Prove that a positive integer n is prime number, if no prime p less than or equal to `sqrtn` divides n.

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RD SHARMA ENGLISH-REAL NUMBERS-All Questions
  1. Find the HCF and LCM of 144, 180 and 192 by prime factorisation method...

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  2. Explain why 7*11*13+13 and 7*6*5*4*3*2*1+5 are composite numbers.

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  3. Prove that a positive integer n is prime number, if no prime p less th...

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  4. Show that every positive even integer is of the form 2q, and that eve...

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  5. prove that there are infinitely many positive integers.

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  6. Determine the prime factorization of each of the following numbers: 13...

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  7. Express each of the following positive integers as the product of its ...

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

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

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

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

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  12. Prove that if x and y are odd positive integers, then x^2+y^2 is even ...

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

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

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

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

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

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

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

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

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