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Use Euclid's division lemma to show that...

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

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MBD-REAL NUMBERS-EXERCISE
  1. Use Euclid's division lemma to show that the square of any positive in...

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  2. Use Euclid's division algorithm to find HCF of : 36,84

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  3. Use Euclid's division algorithm to find HCF of : 34,102

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  4. Use Euclid's division algorithm to find HCF of : 45,75

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  5. Use Euclid's division algorithm to find HCF of : 112,49

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  6. Use Euclid's division algorithm to find HCF of : 4052,12576

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  7. Show that every positive even integer is of the form 2q, for some inte...

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  8. Show that every positive odd integer is of the form 2q + 1, for some i...

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  9. Show that every positive odd integer is of the form 4q + 1 or 4q + 3, ...

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

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  11. Show that one and only one out of p, p + 2 or p + 4 is divisible by 3.

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  12. Renu purchases two bags of fertiliser of weights 75 kg and 69 kg. Find...

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  13. Two tankers contain 434l and 465 litres of diesel respectively. Find t...

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  14. Hotel 'A' has 560 tables. Hotel B' has 400 tables. In each Hotel, the ...

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  15. Use Euclid's division algorithm to find the HCF of 420 and 130.

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  16. Express each number as a product of its prime factors : 32760

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  17. Express each number as a product of its prime factors : 404

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  18. Express each number as a product of its prime factors : 120

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  19. Express each number as a product of its prime factors : 825

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  20. Express each number as a product of its prime factors : 2658

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  21. Find the LCM and HCF of the following pairs of integers and verify tha...

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