MathDB

4

Part of 2024 Czech-Polish-Slovak Junior Match

Problems(2)

Bootstrapping an inequality at integer values

Source: Czech-Polish-Slovak Junior Match 2024, I-4

5/29/2024
Let a,b,ca,b,c be integers satisfying a+b+c=1a+b+c=1 and ab+bc+ca<abcab+bc+ca<abc. Show that ab+bc+ca<2abcab+bc+ca<2abc.
inequalitiesinequalities proposedInteger
How many n are divisible by \lfloor \sqrt{n}\rfloor-1?

Source: Czech-Polish-Slovak Junior Match 2024, T-4

5/29/2024
How many positive integers n<2024n<2024 are divisible by ⌊n⌋−1\lfloor \sqrt{n}\rfloor-1?
number theorynumber theory proposedDivisibilityfloor function