MathDB

4

Part of 2004 May Olympiad

Problems(2)

diophantine system x y z=4104, x+y+z=77

Source: X May Olympiad (Olimpiada de Mayo) 2004 L2 P4

9/19/2022
Find all the natural numbers x,y,zx, y, z that satisfy simultaneously {xyz=4104x+y+z=77\begin{cases} x y z=4104 \\ x+y+z=77 \end{cases}
number theorysystem of equationsdiophantineSystem
given double area, find an angle, squares related (May Olympiad 2004 L1)

Source:

5/11/2019
In a square ABCDABCD of diagonals ACAC and BDBD, we call OO at the center of the square. A square PQRSPQRS is constructed with sides parallel to those of ABCDABCD with PP in segment AO,QAO, Q in segment BO,RBO, R in segment CO,SCO, S in segment DODO. If area of ABCDABCD equals two times the area of PQRSPQRS, and MM is the midpoint of the ABAB side, calculate the measure of the angle ∠AMP\angle AMP.
geometrysqauareareasfind angle