MathDB

2

Part of 2019 Bundeswettbewerb Mathematik

Problems(2)

Six digit number divisible by 271

Source: Bundeswettbewerb Mathematik 2019, Round 1 - Problem 2

8/5/2019
The lettes A,C,F,H,LA,C,F,H,L and SS represent six not necessarily distinct decimal digits so that S≠0S \ne 0 and F≠0F \ne 0. We form the two six-digit numbers SCHLAFSCHLAF and FLACHSFLACHS.
Show that the difference of these two numbers is divisible by 271271 if and only if C=LC=L and H=AH=A.
Remark: The words "Schlaf" and "Flachs" are German for "sleep" and "flax".
DigitsdivisibleDivisibilitynumber theory
min of ab/c+bc/a+ca/b when a,b,c>0 with a^2 + b^2 + c^2 = 1

Source: Germany Federal - Bundeswettbewerb Mathematik 2019 round 2, p2

4/16/2020
Determine the smallest possible value of the sum S(a,b,c)=abc+bca+cabS (a, b, c) = \frac{ab}{c}+\frac{bc}{a}+\frac{ca}{b} where a,b,ca, b, c are three positive real numbers with a2+b2+c2=1a^2 + b^2 + c^2 = 1
inequalitiesminalgebra