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Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.

For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A knot diagram which does not specify whether crossings are under- or overcrossings.

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A mathematical object upon which an operator acts. For example, in the expression 1×2, the multiplication operator acts upon the operands 1 and 2.

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.