MathDB

Problem 4

Part of 1999 Mongolian Mathematical Olympiad

Problems(4)

triangle:A=1999,P=19992 inside triangle:A=2000,P=20002

Source: Mongolia 1999 Grade 8 P4

5/4/2021
Is it possible to place a triangle with area 19991999 and perimeter 1999219992 in the interior of a triangle with area 20002000 and perimeter 2000220002?
geometry
n|2^n+3^n, in/finitude of such n

Source: Mongolia 1999 Grade 9 P4

5/4/2021
Investigate if there exist infinitely many natural numbers nn such that nn divides 2n+3n2^n+3^n.
number theoryDivisibility
N divides phi(p^n-1)

Source: friend

12/12/2005
Maybe well known: pp a prime number, nn an integer. Prove that nn divides ϕ(pn−1)\phi(p^n-1) where ϕ(x)\phi(x) is the Euler function.
Eulernumber theory proposednumber theory
forest growth rate

Source: Mongolia 1999 Teachers elementary level P4

5/6/2021
A forest grows up pp percent during a summer, but gets reduced by xx units between two summers. At the beginning of this summer, the size of the forest has been aa units. How large should xx be if we want the forest to increase qq times in nn years?
ratealgebra