Tag: Number theory

• The Collatz Conjecture: A Problem You Can State in Three Lines and Nobody Can SolveHalve the evens, triple the odds and add one. We prove what can be proved — no short cycles, density 3/4 — and show why the 3n-1 counterexample defeats the probabilistic heuristic.MathematicsMath ColumnsHigh school / generalCollatz conjectureOpen problemsNumber theoryDynamical systems~8 min
• Primes and the Prime Number Theorem: From Infinitude and Unique Factorization to the Law of DistributionFrom divisibility to Euclid's theorem and unique factorization, then Chebyshev-type bounds from binomial coefficients, the prime number theorem, and the open problems beyond it.MathematicsNumber TheoryUndergraduateNumber theoryPrime numbersPrime number theoremUnique factorizationDistribution of primes~7 min