Here is the proof that Pythagoras came to Bharat as student and went back as Teacher.The famous Pythagorean Theorem was not in use for five hundred years after death of Pythagoras. It was Cicero and Plutarch who attributed the theorem to Pythagoras. Roots of mathematics are more ancient than what is taught to you in school. According to Sir Thomas L. Heath, there is no attribution  by Pythagoras himself during his lifetime. The reason I perceive for no attribution is that Pythagoras was groomed in Bharat where knowledge was never copyrighted or attributed to mortals.
Pg 229, “History of European Morals from Augustus to Charlemagne 1913, Part 1 By W. E. H. Lecky, Pythagoras did come to India.
 Euclid (1956). Translated by Johan Ludvig Heiberg with an introduction and commentary by Sir Thomas L. Heath. ed. The Elements (3 vols.). Pg 351