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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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PSEB-REAL NUMBERS -EXERCISE
  1. Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or ...

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  2. An army contingent of 616 members is to march behind an army band of 3...

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  3. Use Euclid's division lemma to show that the square of any positive in...

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  4. Use Euclid's division lemma to show that the cube of any positive inte...

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  5. Express each number as a product of its prime factors : 140

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  6. Express each number as a product of its prime factors : 156

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  7. Express each number as a product of its prime factors: 3825

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  8. Express each number as a product of its prime factors : 5005

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  9. Express each number as a product of its prime factors : 7429

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

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

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

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  13. Find the LCM and HCF of the following integers by applying the prime f...

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  14. Find the LCM and HCF of the following integers by applying the prime f...

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  15. Find the LCM and HCF of the following integers by applying the prime f...

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  16. Given that HCF (306, 657) = 9, find LCM (306, 657).

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  17. Check whether 6^n can end with the digit 0 for any natural number n.

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  18. Explain why 7 xx 11 xx 13 + 13 and 7 xx 6 xx 5 xx4xx3 xx 2 xx 1 + 5 ar...

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  19. There is a circular path around a sports field. Sonia takes 18 minutes...

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  20. Prove that sqrt5 irrational.

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