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In a cyclic quadrilateral ABCD having perpendicular diagonals AC_|_BD, the perpendiculars to the sides through point T of intersection of the diagonals (the anticenter) ...

A pair of positive integers (a_1,a_2) such that the equations a_1+a_2x=sigma(a_1)=sigma(a_2)(x+1) (1) have a positive integer solution x, where sigma(n) is the divisor ...

A numerical knot invariant. For a tame knot K, the bridge index is the least bridge number of all planar representations of the knot. The bridge index of the unknot is ...

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

A Brunnian link is a set of n linked loops such that each proper sublink is trivial, so that the removal of any component leaves a set of trivial unlinked unknots. The ...

Brun's sieve was refined by J. B. Rosser, G. Ricci, and others.

The series producing Brun's constant converges even if there are an infinite number of twin primes, first proved by Brun (1919).

A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* = x (1) x^*y^* = (yx)^* (2) x^*+y^* = (x+y)^* (3) (cx)^* = c^_x^*, (4) where ...

Let K_1 be a torus knot. Then the satellite knot with companion knot K_2 is a cable knot on K_2.

A number n satisfies the Carmichael condition iff (p-1)|(n/p-1) for all prime divisors p of n. This is equivalent to the condition (p-1)|(n-1) for all prime divisors p of n.