MathDB

Problem 1

Part of 2005 Federal Math Competition of S&M

Problems(3)

d+1|n+1 for all d|n (Serbia MO 2005 1st Grade P1)

Source:

4/11/2021
Find all positive integers n with the following property: For every positive divisor dd of nn, d+1d+1 divides n+1n+1.
number theory
QM(a,b)|AM(a,b) implies a=b (Serbia MO 2005 2nd Grade P1)

Source:

4/11/2021
Let aa and bb be positive integers and K=a2+b22K=\sqrt{\frac{a^2+b^2}2}, A=a+b2A=\frac{a+b}2. If KA\frac KA is a positive integer, prove that a=ba=b.
power meanDivisibilityalgebranumber theory
sum x/(√(y+z))>=√(3/2(x+y+z)) in R+

Source: Serbia MO 2005 3&4th Grades P1

4/11/2021
If x,y,zx,y,z are positive numbers, prove that xy+z+yz+x+zx+y≥32(x+y+z).\frac x{\sqrt{y+z}}+\frac y{\sqrt{z+x}}+\frac z{\sqrt{x+y}}\ge\sqrt{\frac32(x+y+z)}.
Inequalityinequalities