hw3 - 6. What is the rightmost digit (digit in the units...

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CSE 321: Discrete Structures Assignment #3 Autumn 2008 Due: Wednesday, October 22 Problems: 1. Prove or disprove: n 2 + 3 n + 1 is always prime for integer n > 0. 2. Prove that if n is an integer then n 2 mod 8 is either 0, 1, or 4. Hint: Consider the different cases of n mod 4. 3. Section 3.4, exercise 22 4. Compute the greatest common divisor for each of the following pairs of numbers. (a) 2 1 · 3 3 · 5 5 , 2 2 · 3 3 · 5 2 (b) 100! , 127 5. Use the Euclidean algortihm to find gcd(2274,174).
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Unformatted text preview: 6. What is the rightmost digit (digit in the units place) of 32 631 ? Show your work. 7. Prove that for any prime p > 3, either p 1 (mod 6) or p 5 (mod 6). 8. Section 3.5, exercise 32 9. Find an inverse of 2 modulo 17. 10. Optional: How many zeroes are there at the end of 100! ? Please write about how many hours it took you to complete this assignment near where you write your name on the rst page....
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