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Mathematics, 30.07.2019 23:20 stace49

Let f(x) = x^{2004} + 2x^{2003} + 3x^{2002} + \dots + 2004x + 2005 and z = cos(pi/1003) + sin (pi/1003). the number [n = f(z)f(z^2) \dotsm f(z^{2005})] can be written in the form a^b, where a and b are positive integers and a is as small as possible. find the remainder when a + b is divided by 1000.

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Let f(x) = x^{2004} + 2x^{2003} + 3x^{2002} + \dots + 2004x + 2005 and z = cos(pi/1003) + sin (pi/10...
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