Let N be a non-zero natural number composed of n digits.

Let us then both prepend and append the number 4 to create two new numbers, 4N and N4, that are both (n+1) digits long.

For example, if N is 123, then we create two numbers: 4123 and 1234.

The question is to find the smallest value of N, such that the following equation holds true:

4N = 4*N4

Again, using the example above, this would require that 4123 = 4*1234.

This is obviously not true, so N=123 is not a solution.

So, find the smallest value of N and its length n.

Bonus:

A generalized question: For which values of K can we find a value

of N (of length n) that solves the general equation KN = K*NK, as defined above?

source: March issue of Science 2.0