Pythagoras’s father was a gem trader from the Levantine coast so the likelihood of him traveling around the Mediterranean is pretty decent. His Egyptian connection is attested early by Herodotus and his devotion to diverse schools of wisdom is attested in a critical statement by his contemporary, Heraclitus.

Of course it’s hard to know. But Plato wrote several letters about his trip to Italy, because he was briefly enslaved there before being freed by his friend the Pythagorean Archytas (who is famous for creating a steam powered flying machine and wrote a work on mechanical engineering). https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1...