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If q>1 is odd the 2q cyclotomic polynomial phi(sub 2q)(x) is equal to

User Martinoss
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Final answer:

The 2q cyclotomic polynomial phi(sub 2q)(x) is equal to x^(4k+2) + x^(4k) + ... + x^4 + x^2 + 1 if q>1 is odd.

Step-by-step explanation:

The 2q cyclotomic polynomial phi(sub 2q)(x) is equal to x^(2q-1) + x^(2q-2) + ... + x^4 + x^2 + 1. Since q>1 is odd, we can simplify the expression further by noticing that q can be written as 2k+1 for some integer k. Substituting q = 2k+1 into the polynomial, we get:



phi(sub 2q)(x) = x^(4k+2) + x^(4k) + ... + x^4 + x^2 + 1



Therefore, if q>1 is odd, the 2q cyclotomic polynomial phi(sub 2q)(x) is given by the expression x^(4k+2) + x^(4k) + ... + x^4 + x^2 + 1

User Jason Siffring
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