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For given positive integers 
$r\ge 3$, 
$n$ and 
$e\le \binom{n}{2}$, the famous Erdős–Rademacher problem asks for the minimum number of 
$r$-cliques in a graph with 
$n$ vertices and 
$e$ edges. A conjecture of Lovász and Simonovits from the 1970s states that, for every 
$r\ge 3$, if 
$n$ is sufficiently large then, for every 
$e\le \binom{n}{2}$, at least one extremal graph can be obtained from a complete partite graph by adding a triangle-free graph into one part.
In this note, we explicitly write the minimum number of 
$r$-cliques predicted by the above conjecture. Also, we describe what we believe to be the set of extremal graphs for any 
$r\ge 4$ and all large 
$n$, amending the previous conjecture of Pikhurko and Razborov.
