Let　f(n)　be　the　maximum　number　of　edges　in　a　graph　on　n　vertices　in　which　no　two　cycles　have　the　same　length.　Erdös　raised　the　problem　of　determining　f(n).　Erdös　conjectured　that　there　exists　a　positive　constant　c　such　that　ex(n,C2k)　≥　cn1+1/k.　Hajos　conjecture　that　every　simple　even　graph　on　n　vertices　can　be　decomposed　into　at　most　n/2　cycles.　We　present　the　problems,　conjectures　related　to　these　problems　and　we　summarize　the　know　results.　We　do　not　think　Hajos　conjecture　is　true.