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Tooth filings pick up AM, not FM. Assuming that’s even a real thing. All you need get AM is a diode which can be made to varying levels of performance with a number of common materials.
FM radios generally use superheterodyne receivers which generate a radio frequency to be mixed with the incoming signal to pull out audio.
This receiver does emit a small amount of RF as a result and it’s how the TV police in the UK would catch you for skirting a TV license.
You should update this article: https://en.m.wikipedia.org/wiki/TV_detector_van#Detection_techniques