### Biography

Federico Villarreal,** **Peruvian mathematician** **and astronomer** **(Túcume, Lambayeque** **31** **August 1850 – Barranco, Lima 03 June 1923)

Authored over 600 works and scientific notes

Developed method to raise any polynomial to any power or Villarreal polynomial (1873)

Enunciated 3 theorems about divisibility criteria being two of them (in Aportes a la teoria de los numeros 1897)

1) the ratio between two numbers represented by same digits in two distinct systems of basis enumeration is divisible by basis difference

2) a number is divisible by a certain divisor if it is the sum of its digits when one write in enumeration system in which the basis is the divisor plus a unit

Obtained a generalization formula for Bernoulli integration formula (1879) in Integración por Traspasos

Obtained a fourth degree differential equation for flexion problem of a truss

Enunciated theorems about inertial moments and central nuclei of regular polygons (1911) in Tratado de Resistencia de Materiales

Discovered embedment moments

Discovered new formulas for studying semiregular solids

First to study the inscribed sphere in edges of regular and semiregular bodies and the sphere that have polyhedral faces as tangential planes

Solved the theoretical problem of disruptive discharge obtaining Thompson formula for oscillations period of a capacitor in Descarga Oscilante en un Condensador (1916)

Developed a simple method for determination of meridian, sun time, geographical latitude and longitude

Metodo para determinar la latitude y longitude de los lugares del Perú (una tecnica sencilla para la determinación de meridianos, la hora solar, las latitudes e longitudes geograficas)

### EPONYMY

Villarreal polynomials

Villarreal child problem (1906)

Villarreal recurring formula