Repdigits

Definition:

http://en.wikipedia.org/wiki/Repdigit

http://mathworld.wolfram.com/Repdigit.html

On Repdigit Polygonal Numbers

http://www.cs.uwaterloo.ca/journals/JIS/keith.html

The Repdigit Prime Problems

http://www.freewebs.com/dries5/prime_problems.htm

Consider the following puzzles:

(1) For which integral values of k is 10^k - 1 the cube of an integer?

(2) Are there any repdigits that are nonagonal numbers?

A nonagonal number is a number of the form k(7k - 5)/2

http://mathworld.wolfram.com/NonagonalNumber.html