If and and is the last digit of the number

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

z + \frac{1}{z} = 1

and

a = z^{2017} + \frac{1}{z^{2017}}

and

b

is the last digit of the number

2^{2^n} - 1

, when the integer

n > 1

, the value of

a^2 + b^2

is (1) 23 (2) 24 (3) 26 (4) 27