In 1998, in the winter issue of the journal Mathematics and Computer
education (see [1]), Monte Zerger posed the following problem. He had noticed
the Pythagorean triple (216,630,666);(216)^2+(630)^2=(666)^2. Note that 216=6^3
and 666 is the hypotenuse length. The question was then, whether there existed
a digit d and a positive integer k(other than the above); such that d^k is the
leglength of a Pythagorean triangle whose hypotenuse length has exactly k
digits, each being equal to d. In 1999, F.Luca and P.Bruckman, answered the
above question in the negative.