Can a pawn put a king in check? I am only an amateur player, but have been playing for many years. Every now and then I come across people who are adamant that a pawn cannot put a king into check.

The last person who I discussed this with was a high school student who played school competitions and pretty much convinced me. So much so that I have now convinced my father, who taught me how to play over 20 years ago that a pawn cannot check or take another piece to put the king into check.

I've just done a Google search to clarify, although most pages say a pawn can put a king into check it has so many results that it has made me curious:

Where did the idea that a king cannot be put in check by a pawn come from?

Are there are competitions / set of rules / types of games where this rule is enforced in the modern game?

Further question, can a pawn also be moved to put a king into checkmate?
Here's a preliminary answer to where such a belief about chess pawns could possibly have come from. In the Japanese variant Shogi, in which an opponent's captured pieces may be placed onto the board as one's own, it is not legal to place down a pawn that gives immediate checkmate. It's still perfectly legal to drop a pawn that gives check though (and to check/mate normally with a pawn), so this a much less severe restriction than what your question asks about. But this is a case in which the pawns are singled out, because any other piece can be dropped to give an immediate checkmate.

Since Shogi and chess are both believed to derive from Chaturanga, perhaps there is indeed some historical variant in which pawns weren't allowed to check at all; but I'm just speculating at the moment.