MathDB

3

Part of 1975 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1975 Problem 1.3

Source: Bundeswettbewerb Mathematik 1975 Round 1

10/21/2022
Describe all quadrilaterals with perpendicular diagonals which are both inscribed and circumscribed.
quadrilateralgeometrydiagonalinscribedcircumscribed quadrilateral
a_n/g_n is a positive integer, then x_1 = x_2 = ··· = x_n

Source: 1975 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p3

11/20/2022
For nnpositive integers x1,x2,...,xn x_1,x2,...,x_n, ana_n is their arithmetic and gng_n the geometric mean. Consider the statement SnS_n: If an/gna_n/g_n is a positive integer, then x1=x2=⋅⋅⋅=xnx_1 = x_2 = ··· = x_n. Prove S2S_2 and disprove SnS_n for all even n>2n > 2.
number theoryarithmetic meangeometric mea