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Show that every even positive integer i...

Show that every even positive integer is of the form 6q or 6q + 2 or 6q + 4 for some integer q .

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Show that any positive integer is of the from 3q or 3q+1 or 3q+2

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Show that any positive integer is of the form 3q or,3q+1 or,3q+2 for some integer q.

Show that every positivee odd integer is the form ( 4q +1) , or ( 4q +3) for some interger q.

Show the every positive odd integer is of the form ( 6m+1) or ( 6m+3) or ( 6m+5) for some intger m.

Show that any positive odd integer is of the form 6q+1 or,6q+3 or ,6q+5, where q is some integer.

Show that the square of any positive integer is either of the form 4q or 4q + 1 form some integer q

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

Prove that if a positive integer is of the form 6q+5, then it is of the form 3q+2 for some integer q, but not conversely.

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NAGEEN PRAKASHAN-REAL NUMBERS-Exercise1 A
  1. Show that any positive odd integer is of the form 4q+1 or 4q+3 , wh...

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  2. Show that any positive integer is of the form 3q or, 3q+1 or, 3q+2 ...

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  3. Show that every even positive integer is of the form 6q or 6q + 2 or...

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  4. Show that every positive integer is either even or odd.

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  5. Proof that the square of any positive integer is of the form of 4m or ...

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

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

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  8. There are 576 boys and 448 girls in a school that are to be divided in...

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  9. The length , breadth and height of a room are 8 m 25 cm , 6 m 75 cm ...

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  10. A sweet seller has 420 kaju barfis and 130 badam barfis. She wants ...

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  11. Two sets of English and social science books containing 336 and 96 res...

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  12. In a group there are 21 childrens, 35 ladies and 49 gents. They all wa...

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  13. Three sets of English, Hindi and Mathematics books have to be stack...

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  14. Find the HCF of 81 and 237 and express it as a linear combination of 8...

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  15. Find the polynomials u(x) and v(x) such that (x^(4) -1) * u(x) + (x^(...

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  16. Six bells commence tolling together and toll at interval of 2, 4 , 6, ...

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  17. Find the greatest number of 4 digits which is exactly divisible by 15 ...

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  18. A number when divided by 143 leaves 31 as remainder. What will be the ...

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  19. p and q are two positive integers such that the least prime factor of ...

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  20. Express each of the following as a product of prime factors: (i) 96 ...

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