foreign key from different tables

I have a table participants and a table projects .
The Primary Keys are:
participants: participant_id
projects: project_id

Between those 2 tables there s a many -many relation.
Therefor I have created a third table called assignment which has in it the columns participant_id and project_id.
This table should have as its key participant_id and project_id which are referring to the columns with same name in the 2 other tables.
I wonder how to write this in MySQL.
I tried many things but no of them worked ..
Thank You much

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