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Unformatted text preview: r ( x ) is a constant r ( x ) = r ∈ Q . (b) Prove that r = f ( c ). 7. Consider the system of equations a + b = 2 m 2 b + c = 6 m a + c = 2 Determine all real values of m for which a ≤ b ≤ c . (This problem is not directly related to the course material, but is included to keep your problem solving skills sharp.) Recommended Problems 1. Text, page 50, #42 2. Text, page 51, #44 3. Text, page 51, #48 4. Text, page 52, #75 5. Text, page 52, #79 ...continued 6. Let a , b and c be non-zero integers. Their greatest common divisor gcd( a, b, c ) is the largest positive integer that divides all of them. (a) If d = gcd( a, b, c ), prove that d is a common divisor of a and gcd( b, c ). (b) If f is a common divisor of a and gcd( b, c ), prove that f is a common divisor of a , b and c . (c) Prove that gcd( a, b, c ) = gcd( a, gcd( b, c ))....
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- Winter '08
- Equations, Linear Diophantine equation, non-negative integer solutions, common divisor gcd