MathDB

There are pairs of square numbers with the following two properties: (1) Their decimal representations have the same number of digits, with the first digit starting is different from

0

. (2) If one appends the second to the decimal representation of the first, the decimal representation results another square number. Example:

16

and

81

;

1681 = 41^2

. Prove that there are infinitely many pairs of squares with these properties.

Problem Statement