What Would You Call A Non-base 10 Decimal?

Let aka_k represent the repeating decimal 0.133k0.\overline{133}_k for k4k \geq 4. The product a4a5a99a_4 a_5 \cdots a_{99} can be expressed as mn!\frac{m}{n!} where m,nm, n are positive integers and nn is as small as possible. mn\frac{m}{n} can be expressed as pq \frac{p}{q} where p,qp, q are coprime integers. What is p+qp+q?

Note: 0.133k0.\overline{133}_k refers to the repeating decimal 0.133133133 0.133133133\ldots evalauted in base kk.

×

Problem Loading...

Note Loading...

Set Loading...