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4023_HW2

# 4023_HW2 - a,b Problem 6 Recall that m Z = mx x ∈ Z the...

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Math 4023 Spring 2011 Homework #2 Read Lax I.2, Number Theory Supplement 1.1,1.2 Problem 1. Exercise 2.7. Problem 2. Exercise 2.12. Problem 3. (a) Calculate d = (4307 , 1121) and express it as a linear combination of 4307 and 1121. (b) Calculate m = [4307 , 1121]. Problem 4. Exercise 2.14. Problem 5. Let a Z such that ( a, 144) = 18 and ( a, 175) = 35. Let b = 3 5 · 5 4 · 7 1 . (a) Compute ( a, b ). (b) What is the highest power of 3 which divides [
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Unformatted text preview: a,b ]? Problem 6. Recall that m Z = { mx : x ∈ Z } , the integer multiples of m . (a) Prove that m Z ∩ n Z = r Z for some r ∈ Z and precisely relate r to n,m . (b) Prove that m Z + n Z = s Z for some r ∈ Z and precisely relate s to n,m . Note that m Z + n Z = { mx + ny : x,y ∈ Z } 1...
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