# How high would it go?

**Number Theory**Level 5

The set A is defined as

\(A=\left\{n|n=\overline{d_kd_{k-1}\cdots d_{1}},n=\sum_{i=1}^k d_i^k\right\}\)

In other words,

\(n\) is a k-digit number which is equal to the sum of the k-th powers of its digits.

Eg : \(153=1^3+5^3+3^3\)

What is the maximum possible number of digits that any number in the set can have?