دنباله ی تعداد مقسوم علیه ها
kafiye az in nokte estefade konid ke agar d(x_{k})=2 bashad angah x_{k} yek adade aval ast va agar d(x_{k-1})=x_{k} bashad chon x_{k} aval ast pas adade x_{k-1} be surate tavani az yek adade aval khahad bud ama tavane an adade aval barabar ba x_{k}-1 khahad bud.
hal do halat darim :
ya x_{k} adadi aval va fard ast ke yani an donbale daraye yek moraba-e kamel khahad bud ...
ya an ke x_{k}=2 ast ama dar chenin halati adade x_{k-1} chon adadi aval be tavane x_{k}-1=2-1=1 ast pas khode x_{k-1} adadi aval ast.
hal hamin estedlal ra baraye adade x_{k-1} va adade x_{k-2} ke d(x_{k-2})=x_{k-1} shode ast be kar mibarim...
pas ba tavajoh be anche ke gofte shod tamamiye adadhaye andonbale bayad barabare do bashand albate avalin adade in donbale mostasnast va mitavanad yek adade avale delkhah bashad...
yani avalin adad: n lazem va kafist ke aval bashad.
pas javab peyda mishavad...
hal do halat darim :
ya x_{k} adadi aval va fard ast ke yani an donbale daraye yek moraba-e kamel khahad bud ...
ya an ke x_{k}=2 ast ama dar chenin halati adade x_{k-1} chon adadi aval be tavane x_{k}-1=2-1=1 ast pas khode x_{k-1} adadi aval ast.
hal hamin estedlal ra baraye adade x_{k-1} va adade x_{k-2} ke d(x_{k-2})=x_{k-1} shode ast be kar mibarim...
pas ba tavajoh be anche ke gofte shod tamamiye adadhaye andonbale bayad barabare do bashand albate avalin adade in donbale mostasnast va mitavanad yek adade avale delkhah bashad...
yani avalin adad: n lazem va kafist ke aval bashad.
pas javab peyda mishavad...
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