Show that the sequence, $49, 4489, 444889, \dots$, gotten by inserting the digits $48$ in the middle of the previous number (all in base $10$), consists only of perfect squares.
has become a classic. For some reason, I got curious as to who actually discovered this.
After doing some research, seems like this problem was used in the Stanford University Competitive Exam in Mathematics for high school seniors, in the year 1964. One pdf which has this is here: http://www.computing-wisdom.com/jstor/stanford-exam.pdf. It appears as problem 64.2.
The pdf also mentions that there is a booklet which gives references to previous appearances of the problems from the above exam, but that seemed to be a dead-end regarding this particular problem.
Does anyone know who originally discovered this little gem? More interestingly, is it known how this was discovered?
On some more research I found this book from 1903: Algebra Part II by E.M. Langley and S.R.N. Bradly which has this as an exercise on page 180. The question seems to have been phrased in such a way as to claim ownership and also tells how it was discovered. I guess we just need confirmation now.
More digging reveals this German book by Dr. Hermann Schubert, Mathematische Mussestunden, which has this on page 24. The book was published in 1900, but the preface seems to be dated earlier. If someone can read German, perhaps maybe they can read and see what the book claims about the origins of this problem. The book seems to have a list of references at the beginning.