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Assign1 - MATH 135 Assignment#1 Winter 2009 Due Wednesday...

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MATH 135 Winter 2009 Assignment #1 Due: Wednesday 14 January 2009, 8:20 a.m. N.B. Assignments 3 to 9 will not be distributed in class. You must download them from the course Web site. Hand-In Problems 1. Disprove the statement “There is no integer n > 3 such that 2 n 2 + 1 is a perfect square”. 2. (a) Treating the equation 2 x 2 + xy + y +3 x +2 = 0 as a quadratic equation in x with coefficients in terms of y , solve for x . (b) Is the statement “For all real numbers x and y , 2 x 2 + xy + y + 3 x + 2 negationslash = 0” true or false? Justify your answer. 3. Prove that sin 4 x sin 2 x = cos 4 x cos 2 x for all real numbers x . 4. Prove that if 3 x 6, then 6 x 2 5 x 6. 5. Prove that if n is a positive integer and n 2 written in digital form ends in 9, then n written in digital form ends in 3 or 7. 6. Prove that if n is a positive integer which is not divisible by 3, then n 2 1 is divisible by 3. 7. To prove a statement of the form “ A if and only if B ”, we need to prove two statements: “If A then B
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