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Solution 6(repeated)  by slayerchange

  We want: Now, observe that for , which is not the case , Same observation holds for Let n be even and Same operation for is not the case since S might contain odd power of x. Suppose S does not contain odd power.Then However, S does not contain odd power means , Answer : I) for degree n P(x) , necessary condition is P(x)=xn II)Up to degree n polynomials,there are P(x)=c , P(x)=xi for in,i is fixed.

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