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accepted actual added American Mathematical Monthly angles appear approach argument assertion assume Bussey called conclusions Consider contains contains a least deductive definition disc divisible equal example exists Find formula geometry girls given gives grade greater guess high school hypothesis Illustration implies included Initial step integers interesting introduced involved kinds later least element logic mathematical induction measures mentioned method move natural numbers ninth obtain Origin Perhaps pieces polygon positive integral values possible preceding principle of mathematical problems proof Property Proposition prove reasoning recursive References remember require roubles rule sequence Sequential step shown sides smaller solutions square number statement step student suggest Suppose Table Teachers term theorem topic Tower transfer triangle triangular true for n=k truth valid