Is there a positive integer whose repeat is a perfect square? If so, how many such integers exist?

Question

The repeat of a positive integer is obtained by writing it twice in a row (so, for example, the repeat of 2017 is 20172017)

Answer

One digit: x + 10x = 11x No root satisfies the requirement.
Two digits: x + 100x = 101x &radic;101 = 10.0498752 there is no number to get an integer.
Three digits: x + 1000x = 1001x You can see where this is going.

Is there a positive integer whose repeat is a perfect square? If so, how many such integers exist?

Answers (1)