Diophantine Memes

The sunglasses come off when things get serious! The first statement "√2 is irrational" is basic math knowledge - no biggie. But mention that "a² = 2b² is insoluble in integers" and suddenly we're in mind-blown territory. What's the joke? These statements are actually equivalent! The irrationality of √2 means precisely that the equation a²=2b² has no integer solutions (where a and b have no common factors). Leopold Kronecker, the mathematician referenced in the title, was famously obsessed with integers, once declaring "God made the integers, all else is the work of man." He'd definitely appreciate this integer-focused humor!

Congratulations! You've encountered the rare fruit-based mathematical puzzle that's somehow harder than proving the Riemann hypothesis. The equation suggests apple + mango = orange, while the bottom shows apple, mango, orange, pineapple ∈ N (meaning they're all natural numbers), with pineapple > 2. It's essentially a system of Diophantine equations disguised as produce. The 99.9% statistic is generous—even my calculator just threw itself out the window. The only people solving this are either Fields Medalists or those who realize it's completely made up to make you feel inadequate about your fruit-counting abilities.