problem number theory problem asks sets property set proper product set plus problem named mathematician suggested considered similar problems time closely related problem drops assumption called improper problem solution improper problem easily provided terms sequence required property sun showed solution proper problem sun solution based similar sequence different set initial values problem closely related egyptian known solutions fixed unknown solutions problem odd numbers remain open questions problem problem asks sets property set proper product set plus given sets formula divides equal formula closely related problem concerns sets set necessarily proper plus product set problem named literature referred improper problem solution problem solution improper problem necessarily vice versa history problem named mathematician suggested posed improper problem independently found solutions improper problem showed problem credited finding solution examples solution calculations interesting near miss set formed taking terms sequence property set divides product set plus member set equal product members plus proper solution improper problem solution problem usually defined connection egyptian solution improper problem equivalent division product solution equation formula conversely solution corresponds solution improper problem known solutions satisfy equation formula lead egyptian fraction representation number sum unit cited papers problem study solutions equation describe application equation classification surfaces describe application theory finite number solutions showed number solutions finite makes sense count total number solutions calculated number solutions small values starting forms sequence sequence presently solutions known unclear solutions remain values infinitely solutions fixed showed solutions improving earlier results proving existence fewer solutions number solutions value grows unknown solutions problem odd numbers exception known solutions start numbers solution problem improper problem prime product primary number unknown infinitely solutions type exist
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