Higher Algebra : a Sequel to Elementary Algebra for Schools
The book Higher Algebra : a Sequel to Elementary Algebra for Schools was written by author H S Henry Sinclair Hall Here you can read free online of Higher Algebra : a Sequel to Elementary Algebra for Schools book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Higher Algebra : a Sequel to Elementary Algebra for Schools a good or bad book?
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Prove that 2 4 ' 1 - 1 is divisible by 15. 9. Prove that n (?i + 1) (n + 5) is a multiple of 6. 10. Shew that every number and its cube when divided by 6 leave the same remainder. 11. If n is even, shew that n (;i 2 + 20) is divisible by 48. 12. Shew that n (?i 2 - 1) (Sn + 2) is divisible by 24. 13. If n is greater than 2, shew that n 5 — 5n 3 -f 4?i is divisible by 120. 14. Prove that 3 2n + 7 is a multiple of 8. 15. If n is a prime number greater than 3, shew that ?i 2 - 1 is a multiple of 2...4. 16. Shew that n 5 — n is divisible by 30 for all values of n, and by 240 if n is odd. 17. Shew that the difference of the squares of any two prime numbers greater than 6 is divisible by 24. 18. Shew that no square number is of the form 3?i — 1. 19. Shew that every cube number is of the form 9?i or 9n±L THEORY OF NUMBERS. 349 20. Shew that if a cube number is divided by 7, the remainder is 0, 1 or 6. 21. If a number is both square and cube, shew that it is of the form 7n or 7?t+l. 22. Shew that no triangular number can be of the form 3u - 1.
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