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Erdos, Faudree and Rousseau conjectured in 1992 that for every  $k\ge 2$ every graph with n vertices and $n^2/4+1$ edges contains at least  $2n^2/9$ edges that occur in $C_{2k+1}$. Very recently, Furedi and Maleki  constructed n-vertex graphs with more than $n^2/4$ edges such that only  $(2+\sqrt{2}+o(1))n^2/16\approx0.213n^2$ of them occur in $C_5$, which disproves  the conjecture for $k=2$.. With Grzesik and Volec, we use a different approach  to tackle this problem and obtain exact result. We adapt the approach to show  that the conjecture is true for $k\ge 3$.