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A conjecture which relates the minimal elliptic discriminant of an elliptic curve to the j-conductor. If true, it would imply Fermat's last theorem for sufficiently large ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...