* Fermat's Little Theorem and Sophie's Proof

* Ideal Numbers, Proof that the theory of ideal numbers saves unique factorization for cyclotomic integers at Fermat's Last Theorem Blog.

* " Perpetuum Mobile " was used in the 1997 award-winning BBC Horizon documentary " Fermat's Last Theorem " directed by Simon Singh ( shown in North America as part of the PBS series ' Nova ' entitled " The Proof ").

Proof of ( 1 ) and ( 2 ): One has from Fermat's little theorem,

Because of its picturesque surroundings Stowe has been the setting for many films, including Indiana Jones and the Last Crusade, the Bollywood film Kabhi Khushi Kabhi Gham, Proof of Life, Stardust ( 2007 ), and The World Is Not Enough in the James Bond series.

* Proof of Wedderburn's Theorem at Planet Math

A more successful effort was the Standard Proof for Pythagoras ' Theorem, that replaced the more than 100 incompatible existing proofs.

Proof ( Theorem )

* 19-" Non-Standard Models and Godel's Theorem: A Model-Theoretic Proof of Godel's Theorem ".

* Proof of Dehn's Theorem at Everything2

* Feuerbach's Theorem: a Proof at cut-the-knot

* Feuerbach's Theorem: a Proof

* A Proof of the Pythagorean Theorem From Heron's Formula at cut-the-knot

* James Gregory's Euclidean Proof of the Fundamental Theorem of Calculus at Convergence

* The Proof of the Gibbard – Satterthwaite Theorem Revisited

* Murray Eisenberg, Robert Guy, A Proof of the Hairy Ball Theorem, The American Mathematical Monthly, Vol.

* A Visual Proof of Girard's Theorem by Okay Arik, the Wolfram Demonstrations Project.

*" Claim of Proof to Four Colour Theorem.

* A Proof of the Borel – Weil – Bott Theorem, by Jacob Lurie.

In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize of the Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem.

* A Proof of Menger's Theorem

* Lovell, M., 2008, A Simple Proof of the FWL ( Frisch, Waugh, Lovell ) Theorem, Journal of Economic Education.

Proof: By symmetry, it suffices to prove that there is some constant c such that for all bitstrings s

Generally this is in a very small detail, such as the number of leaves on the ear of corn on the recent US Wisconsin state quarter: File: 2004 WI Proof. png.

From the criterion it also follows that Carmichael numbers are cyclic .< ref > Proof sketch: If is square-free but not cyclic, for two prime factors and of.

* Demonstratio evangelica ( Proof of the Gospel ) is closely connected to the Praeparatio and comprised originally twenty books of which ten have been completely preserved as well as a fragment of the fifteenth.

He famously put the point into dramatic relief with his 1939 essay " Proof of an External World ", in which he gave a common sense argument against scepticism by raising his right hand and saying " Here is one hand ," and then raising his left and saying " And here is another ," then concluding that there are at least two external objects in the world, and therefore that he knows ( by this argument ) that an external world exists.

Proof of second property: since a * b and b * b < sup >− 1 </ sup > are defined, so is a * b * b < sup >− 1 </ sup >=

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

#* Proof: suppose that p is composite, hence can be written with a and Then is prime, but and contradicting statement 1.

#* Proof:, so is a square root of 2 modulo.

* In Hal Clement's short story Proof ( 1942 ), neutronium is the only form of solid matter known to Solarians, the inhabitants of the Sun's interior.

Proof: If there is no possible move, then the lemma is vacuously true ( and the first player loses the normal play game by definition ).

Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.

( Proof: either 1 is positive or − 1 is positive.

Proof by contradiction is also known as indirect proof, apagogical argument, proof by assuming the opposite, and reductio ad impossibilem.

* Proof that R is uncountable

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

Proof: We only give the proof in the simplified case ; the general case is similar.

This improvement was discovered by Darsey of the Parker Rust Proof Company, who filed a patent in February 1941, which was granted in August 1942,, that improved upon the zinc phosphatizing ( Parkerizing ) process further.

In 1924, there were rumours that gold had been discovered close to the Rabbit Proof fence and the town of Holleton was established about 50 km from Narembeen, but Narembeen prospered as it was the closest train station to Holleton and offered a motor transport service to the miners.

That he Fraunces was the Person that first discovered the Conspiracy which was formed in the Year 1776 against the Life of his Excellency General Washington and that the Suspicions Which were Entertained of his agency in that Important Discovery accationed occasioned a public Enquiry after he was made a Prisoner on which the want of positive Proof alone preserved his Life.