The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which...

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which happens to be positive. This real number a satisfies the following properties:

- for i = 1,2,3,4,5,6,7,8,9,10, one has {a^i} not equal to zero

- one has

[a] = 1, [a^2] = 3, [a^3] = 6, [a^4] = 11, [a^5] = 21, [a^6] = 7, [a^7] = 71, [a^8] = 130

(for a real number x, [x] denotes the floor of x and {x} denotes the fractional part of x.)

find this real root a

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Colby Messinger answered 2 years ago

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