Benno, do you know who Ring Lardner was? If you don't, look him up and look up his book You Know Me, Al. There's a great classic line in the book. "Shut up, he explained."
So, shut up and accept that f/a @ shutter speed b will have the same effect on film for all focal lengths, subject to the lenses used having the same transmission. Not all lenses transmit the same fraction of the light that strikes their front elements.
More seriously, Emmanuel Bigler posted a thorough explanation of the math behind the assertion somewhere on this site. Your next assignment is to find it.
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