MathDB

3

Part of 2012 South East Mathematical Olympiad

Problems(2)

composite number

Source: China south east mathematical Olympiad 2012 day1 problem 3

7/17/2013
For composite number nn, let f(n)f(n) denote the sum of the least three divisors of nn, and g(n)g(n) the sum of the greatest two divisors of nn. Find all composite numbers nn, such that g(n)=(f(n))mg(n)=(f(n))^m (m∈N∗m\in N^*).
number theory unsolvednumber theory
find the size of angle AME

Source: China south east mathematical Olympiad 2012 day2 problem 7

7/17/2013
In △ABC\triangle ABC, point DD lies on side ACAC such that ∠ABD=∠C\angle ABD=\angle C. Point EE lies on side ABAB such that BE=DEBE=DE. MM is the midpoint of segment CDCD. Point HH is the foot of the perpendicular from AA to DEDE. Given AH=2−3AH=2-\sqrt{3} and AB=1AB=1, find the size of ∠AME\angle AME.
trigonometrygeometrycircumcirclegeometry unsolved