(number theory) the theorem that states that every integer greater than one is uniquely expressible as a product of prime numbers, which is called its prime factorization

(geometry) A theorem stating that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.

(number theory) A theorem stating that, if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.

(geometry) A theorem which states that, in 3-dimensional space, any displacement of a rigid body such that some point on it remains fixed is equivalent to a single rotation about some axis that runs through said point.

(mathematics) A theorem in complex analysis concerning the existence of meromorphic functions with prescribed poles.

(mathematics) A theorem stating that a polynomial ring over a Noetherian ring is Noetherian.

(physics) A theorem that states the moment of inertia of a rigid body about any axis is equal to its moment of inertia about a parallel axis through its center of mass plus the product of the mass of the body and the square of the distance between the two parallel axes.

(physics) A theorem that states the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point where the perpendicular axis passes through it.

(mathematics) A theorem stating that every finite group of odd order is solvable.

(mathematics) A theorem that establishes the transcendence of a large class of numbers, stating that, if a and b are algebraic numbers with a ≠ 0, 1, and b irrational, then any value of aᵇ is a transcendental number.