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test2-fall94

# test2-fall94 - J a:= ka k ∈ Z Then J a is an ideal of Z 6...

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Name: S.S.N: MAS 3300 – Test 2 Fall 1994 When giving proofs quote the relevant axioms and results. The questions have equal value. Write on ONE side of your paper. 1. If a is any integer then 1 | a . 2. If a , b , c are integers, and a | b and b | c , then a | c . 3. Let J be an ideal of Z . If x J then - x J . 4. For any integer n 1 we have 1 · 2 · 3 · 4 + 2 · 3 · 4 · 5 + 3 · 4 · 5 · 6 + . . . + n ( n + 1)( n + 2)( n + 3) = 1 5 n ( n + 1)( n + 2)( n + 3)( n + 4) . 5. Let a be an integer and define
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Unformatted text preview: J a := { ka : k ∈ Z } . Then J a is an ideal of Z . 6. Suppose a , b , c are integers. If a | bc , and the two numbers a and b are relatively prime then a | c . 7. Let a , b , c be integers and suppose a , b are not both zero. Let d = gcd( a,b ). Then ax + by = c for some integers x and y , if and only if d | c . 1...
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