The following solution was recieved from Andrei of School 205 Bucharest. Well done and thank you Andrei.

10201 could be written (in base x) as:

10201 = 1x0 + 2x2 + 1x4 = x4 + 2x2 + 1 = (x2 + 1)2

Now, I write 10101 in a similar manner, in base y:

10101 = y4 + y2 + 1 = y4 + 2y2 − y2 + 1 = (y4 + 2y2 + 1) − y2 = (y2 + 1)2 − y2 = (y2 + 1 + y)(y2 + 1 −y)

Therefore both expressions can be factorised, so they are composite.