How well do you know 2017?\sqrt{2017}?

Algebra Level 4

f(x)={0+β : x0mod31+β : x1mod32+β : x2mod3f(x) = \begin{cases} 0 + \beta \ : \ \lfloor x \rfloor \equiv 0 \mod 3 \\ 1 + \beta \ : \ \lfloor x \rfloor \equiv 1 \mod 3 \\ 2 + \beta \ : \ \lfloor x \rfloor \equiv 2 \mod 3 \\ \end{cases}

There is a unique value of β\beta such that n=1f(3n2017)3n=0.\displaystyle \sum_{n=1}^{\infty} \frac{f \left( 3^{n}\sqrt{2017} \right)}{3^{n}} = 0. This value of β\beta can be expressed as abc, a-b\sqrt{c}, where a, b,a,\ b, and cc are positive integers and cc is square-free. Find a+b+c. a + b + c .

×

Problem Loading...

Note Loading...

Set Loading...