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Unformatted text preview: books remain to be put on the last shelf. On the other hand, the last shelf will only contain 1 book if you put 6 or 7 books on each of the other shelves with all shelves containing the same number of books. How many books do you have? 5 PROBLEM 5 a. (4 pts) Convert (23 . 875) 10 to binary. Show your work. b. (6 pts) Carry out the following operations in binary number system: i. (3 pts) 110001 . 01 − 1011 . 11. ii. (3 pts) 1111 × 10101. 6 PROBLEM 6 Using less than 8 divisions determine whether the number 293 is prime. Show your work. 7 PROBLEM 7 a. (5 pts) Use Fermat’s Little Theorem to ﬁnd 7 62 mod 13. b. (5 pts) Show that 1 ° + 2 ° + 3 ° + ⋅⋅⋅ + ( ° − 1) ° ≡ 0 mod ° for any prime ° > 2. ( Hint : ∑ ± ² =1 ± = ² ( ² + 1) / 2) 8...
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 Spring '08
 Staff
 Statistics, Binary numeral system, Decimal, Prime number, Prof. Ananth Grama

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