The general solution is in the form of x =
−750 + 26t, y = 750 − 25t where t is an integer. If x > 0 and y > 0, then
28 22
26 < t < 30. Since t must be integer, we conclude that t = 29. Therefore,
the Diophantine equation has only a positive solution x = 4 and y = 25.