Gurzadyan theorem
In cosmology, Gurzadyan theorem, proved by Vahe Gurzadyan, states the most general functional form for the force satisfying the condition of identity of the gravity of the sphere and of a point mass located in the sphere's center. This theorem thus refers to the first statement of Isaac Newton’s  shell theorem (the identity mentioned above) but not the second one, namely, the absence of gravitational force inside a shell. The theorem had entered, for example, in physics manual website and its importance for cosmology outlined in several papers   as well as in shell theorem. The formula and the cosmological constant 
The formula for the force derived in   has the form

where  and  are constants. The first term is the familiar law of universal gravitation, the second one corresponds to the cosmological constant term in general relativity and McCrea-Milne cosmology. Then the field is force-free only in the center of a shell but the confinement (oscillator) term does not change the initial  symmetry of the Newtonian field. Also, this field corresponds to the only field possessing the property of the Newtonian one: the closing of orbits at any negative value of energy, i.e. the coincidence of the period of variation of the value of the radius vector with that of its revolution by  (resonance principle) . Consequences: cosmological constant as a physical constant  

Einstein named the cosmological constant as a universal constant, introducing it to define the static cosmological model. From this theorem the cosmological constant  emerges as additional constant of gravity along with the Newton’s gravitational constant . Then, the cosmological constant is dimension independent and matter-uncoupled and hence can be considered even more universal than Newton’s gravitational constant. For  joining the set of fundamental constants , the gravitational
Newton’s constant, the speed of light and the Planck constant, yields

and a dimensionless quantity emerges for the 4-constant set 

where  is a real number. Note, no dimensionless quantity is possible to construct from the 3 constants . This within a numerical factor, , coincides  with the information (or entropy) of de Sitter event horizon 

and the Bekenstein Bound

Rescaling of physical constants 

Within the Conformal Cyclic Cosmology   this theorem implies that, in each aeon of an initial value of , the values of the 3 physical constants will be eligible for rescaling fulfilling the dimensionless ratio of invariants with respect to the conformal transformation  

Then the ratio yields 

for all physical quantities in Planck (initial) and de Sitter (final)  eras of the aeons, remaining invariant under conformal transformations. Inhomogeneous Fredholm equation
This theorem, in the context of nonlocal effects in a system of gravitating particles, leads to the inhomogeneous Dirichlet boundary problem for the Poisson equation

where   is the radius of the region,
. Its solution can be expressed in terms of the double layer potential, which leads to an inhomogeneous nonlinear Hammerstein integral equation for the gravitational potential

This leads to a linear inhomogeneous 2nd kind Fredholm equation

Its solution can be expressed in terms of the resolvent  of the integral kernel and the non-linear (repulsive) term

Observational indications 
The dynamics of groups and clusters of galaxies are claimed to fit the theorem, see also. The possibility of two Hubble flows, a local one, determined by that formula, and a global one, described by Friedmannian cosmological equations was stated in. References 

Eponymous theorems of physics
Gravity
Mathematical theorems