With the trials/HSC season approaching (in one year), I've composed a problem that I think is a perfect "final boss" challenge for those aiming for the top of the state. It’s a beautiful walkthrough of the proof that ζ(3) is irrational.
Why you should try this:
The Challenge:
The problem guides you through an irrationality criterion, a 3-variable optimization, and an integral construction that eventually forces a contradiction.
Good luck to everyone grinding through Extension 2! Post your solutions or where you’re getting stuck below. Let’s see who can crack the logic for the final contradiction first.
Why you should try this:
- Problem 16 Vibes: This is classic "Question 16" material - it's non-routine, deeply conceptual, and honestly a bit harder than the Q16s we’ve seen in the last few years.
- The "Top 0.001%" Test: If you can navigate the reasoning behind these four parts without getting lost in the algebra, you’re in a very strong position for a U4.
- Focus on Logic: The "heavy lifting" (the massive integral evaluations and LCM bounds) is already provided as hints. Your job is to connect the dots and provide the rigorous reasoning that bridges these complex results.
The Challenge:
The problem guides you through an irrationality criterion, a 3-variable optimization, and an integral construction that eventually forces a contradiction.
Good luck to everyone grinding through Extension 2! Post your solutions or where you’re getting stuck below. Let’s see who can crack the logic for the final contradiction first.