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rama rao Grade: 10
        determine all positive integers n such that the polynomial with n+1 terms f(x)=(xpower 4n)+xpower 4(n-1)+....+xpower8+(xpower4)+1 is divisible by g(x)=(xpower 2n)+xpower 2(n-1)+....+xpower4+xpower2)+1.
6 years ago

Answers : (2)

Chetan Mandayam Nayakar
312 Points
										

both f(x) and g(x) are geometric progressions. for f(x) and g(x),a=1,for f(x), r=x4, for g(x), it is x2


f(x)/g(x)=((1-x4(n+1))/(1-x4))((1-x2(n+1))/(1-x2))=(1+x2(n+1))/(1+x2), it is clear from algebra that n+1 is odd, implying that n is any even natural number


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6 years ago
Chetan Mandayam Nayakar
312 Points
										

both the num(numerator) and den(denominator) are simple geometric progressions


num/den= ((1-x4(n+1))/(1-x4))(1-x2)/(1-x2(n+1)) = (1+x2(n+1))/(1+x2)


obviously n+1 is odd which implies that n is any even natural number

6 years ago
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