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Show that the square of any positive int...

Show that the square of any positive integer cannot be of the form 5m + 2 or 5m +3 for some integer m .

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where q is any positive integer
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OSWAL PUBLICATION-REAL NUMBERS-NCERT Corner (Exercise - 1.3)
  1. By using the method of contradiction verify that P: sqrt(5) is irratio...

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  2. Prove that 3 + 2 sqrt(5) is an irrational number

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  3. 1/sqrt2 is

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  4. Prove that the following irrationals ? 7 sqrt(5)

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  5. Prove that the following irrationals ? 6 + sqrt(2)

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  6. Show that the square of any positive integer is either of the form 4q...

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  7. Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3...

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  8. Show that the square of any positive integer cannot be of the form 5m ...

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  9. Show that the square of any positive integer cannot be of the form 6m+...

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  10. Show that the square of any odd integer is of the form 4m+1, for some ...

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  11. If n is an odd integer, then show that n^(2) - 1 is divisible by 8

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  12. Prove that if x and y are both odd positive integers then x^(2) + y^...

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  13. Use Euclid division algorithm to find the HCF of 441, 567 and 693.

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  14. Using Euclid's division algorithm, find the largest number that divide...

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  15. Prove that sqrt(3)+\ sqrt(5) is an irrational number.

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  16. Show that 12^n cannot end with the digits 0 or 5 for any natural numbe...

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  17. In a morning walk, three persons step off together and their steps mea...

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  18. Write the denominator of the rational number 257/5000 in the form 2^m ...

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  19. Prove that sqrtp+sqrtq is an irrational, where p and q are primes.

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