MathDB

P3

Part of 2023 Bangladesh Mathematical Olympiad

Problems(2)

Weird diophantine equation

Source: BdMO 2023 Secondary National P3

2/12/2023
Solve the equation for the positive integers: (x+2y)2+2x+5y+9=(y+z)2(x+2y)^2+2x+5y+9=(y+z)^2
number theoryDiophantine EquationsfactorizationDiophantine equation
Smallest Positive Integer

Source: BdMO 2023 Higher Secondary National P3

2/12/2023
For any positive integer nn, define f(n)f(n) to be the smallest positive integer that does not divide nn. For example, f(1)=2f(1)=2, f(6)=4f(6)=4. Prove that for any positive integer nn, either f(f(n))f(f(n)) or f(f(f(n)))f(f(f(n))) must be equal to 22.
functionnumber theory