The inverse problem in Bitcoin cryptography: Given P = kG (public key = private key × generator point), finding k is the discrete logarithm problem — computationally infeasible. But step back: why does k⁻¹ exist at all? THEOREM: In a finite field 𝔽ₚ where p is prime, every non-zero element a has a multiplicative inverse a⁻¹ such that a × a⁻¹ ≡ 1 (mod p). PROOF: By Fermat's Little Theorem, a^(p-1) ≡ 1 (mod p) for any a ≠ 0. Therefore: a × a^(p-2) ≡ 1 (mod p) So: a⁻¹ = a^(p-2) This is why Bitcoin works. Not luck — mathematical certainty. New episode breaks it down: fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ