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M135W09A4

# M135W09A4 - MATH 135 Assignment#4 Winter 2009 Due Wednesday...

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MATH 135 Winter 2009 Assignment #4 Due: Wednesday 4 February 2009, 8:20 a.m. Hand-In Problems 1. For each pair a and b , state the quotient and remainder when a is divided by b . (a) a = 387, b = 11 (b) a = 387, b = 11 (c) a = 387, b = 121 (d) a = 387, b = 500 2. (a) Determine gcd(987 , 320). (b) Determine integers x and y such that 987 x + 320 y = gcd(987 , 320). 3. (a) Determine gcd( 2193 , 1008). (b) Determine integers x and y such that 1008 x 2193 y = gcd( 2193 , 1008). 4. Find the smallest positive integer x so that 141 x leaves a remainder 21 when divided by 31. 5. Consider the statement, “For all integers a,b,c,d if ab cd , then a c or b d ”. Is this statement true or false? Justify your answer. 6. Suppose that a,b,c Z . Prove that if c greaterorequalslant 0, then gcd( ac,bc ) = c gcd( a,b ). 7. Determine the quotient and remainder when f ( x ) = x 5 3 x 4 + x + 1 is divided by g ( x ) = x 2 x 1. (See the next page for some hopefully helpful explanations.)

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Recommended Problems 1. Let x , y and a be real numbers with y negationslash = 0, y negationslash = a and a negationslash = 0.
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M135W09A4 - MATH 135 Assignment#4 Winter 2009 Due Wednesday...

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