If is an odd integer and

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

If n>0n > 0 is an odd integer and x=(2+1)n,f=x−[x]x = (\sqrt{2} + 1)^n, f = x - [x] , then f1−f2\frac{f}{1-f^2} is (1) an irrational number (2) a non-integer rational number (3) an odd number (4) an even number

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