Tag Archives: induction

MaBloWriMo 7: s via omega

Yesterday, I challenged you to prove that where , , and the are defined by and . The proof is by induction on . The base case is just arithmetic: Now suppose that we already know the statement holds for … Continue reading

Posted in algebra, arithmetic, iteration, modular arithmetic, number theory | Tagged , , , , , , , | 11 Comments

More hyperbinary fun

When I originally posed Challenge #12, a certain Dave posted a series of comments with some explorations and partial solutions to part II (the hyperbinary sequence). Although I gave the “solution” in my last post, no solution to any problem … Continue reading

Posted in challenges, induction, pattern, proof, recursion, sequences, solutions | Tagged , | 12 Comments