MathDB

4.2

Part of 2011 Saudi Arabia Pre-TST

Problems(2)

computational geo with cyclic pentagon

Source: 2011 Saudi Arabia Pre-TST November 4.2

12/31/2021
Pentagon ABCDEABCDE is inscribed in a circle. Distances from point EE to lines ABAB , BCBC and CDCD are equal to a,ba, b and cc, respectively. Find the distance from point EE to line ADAD.
pentagonCyclicgeometry
sum a_k (k!)^{2010}= (2011 !)^{2010}

Source: 2011 Saudi Arabia Pre-TST February 4.2

1/1/2022
Find positive integers a1<a2<...<a2010a_1 < a_2<... <a_{2010} such that a1(1!)2010+a2(2!)2010+...+a2010(2010!)2010=(2011!)2010.a_1(1!)^{2010} + a_2(2!)^{2010} + ... + a_{2010}(2010!)^{2010} = (2011 !)^{2010}.
number theoryfactorial