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A :

(1) Show that f(x)=x2 is not the sum of two periodic functions.

(2) Show that it *is* the sum of three periodic functions.

This is related to a post of @davidradcliffe's and a post of mine:
mathstodon.xyz/web/@davidradcl
mathstodon.xyz/web/@PedanticOw

I'll toot answers tomorrow, if needed.