MathDB

3

Part of 2016 May Olympiad

Problems(2)

sum of squares of digits divides May Olympiad (Olimpiada de Mayo) 2016 L2 P3

Source:

9/25/2021
We say that a positive integer is quad-divi if it is divisible by the sum of the squares of its digits, and also none of its digits is equal to zero. a) Find a quad-divi number such that the sum of its digits is 2424. b) Find a quad-divi number such that the sum of its digits is 10011001.
Digitsnumber theorydivides
Weird Problem

Source: May Olympiad(Olimpiada de Mayo) 2016

10/2/2017
In a triangle ABCABC, let DD and EE point in the sides BCBC and ACAC respectively. The segments ADAD and BEBE intersects in OO, let rr be line (parallel to ABAB) such that rr intersects DEDE in your midpoint, show that the triangle ABOABO and the quadrilateral ODCEODCE have the same area.
geometrymidpoints