4383_HW06_Sp12

4383_HW06_Sp12 - ( 29 6614 857 5 12 1 mod7- . 5. If a and b...

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Number Theory Spring 2012 Homework 6 Sections 4.4 and 5.2 1. Show that if p is an odd prime number, then ( 29 ( 29 1 2 3 ... 1 0 mod + + + + - p p p p n p . 2. Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives a remainder of 4 in each case. 3. Section 4.4 Problem # 18 (show your work!) 4. Show that
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Unformatted text preview: ( 29 6614 857 5 12 1 mod7- . 5. If a and b are positive integers such that gcd(ab, 70) = 1, show that ( 29 12 12 0 mod 280- a b . 6. Section 5.2 Problem #2(a) 7. Section 5.2 Problem # 6 8. Section 5.2 Problem # 7 9. Section 5.2 Problem # 9(a) 10. Section 5.2 Problem # 14...
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