His proof of this theorem is one of those cases. Below is a proof closer to that which Euclid wrote, but still using our modern concepts of numbers and proof. See David Joyce's pages for an English translation of Euclid's actual proof. Theorem. There are more primes than found in any finite list of primes. Proof. The theorem of the title has been known for centuries, perhaps longer, but I believe that Lagrange gave the first proof. When I was a student, I saw a very different (and, in my opinion, harder) proof from the one given here. I don't know who discovered this proof, but I saw it in Alan Baker's little book on number theory.

Remainder theorem definition is - a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x First Known Use of remainder theorem. 1886, in the meaning defined above.On the remainder in the Taylor theorem ... We give a short straightforward proof for the bound of the reminder term in the Taylor theorem. The proof uses only ...

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