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Claim. The Theorem (p. 123) of P. Erdős, On a theorem of Rademacher-Turán, Illinois J. Math. 6 (1962), no. 1, 122--127: there is an absolute constant $c_1>0$ such that for $t<c_1n/2$ every graph on $n$ vertices with $\lfloor n^2/4\rfloor+t$ edges has at least $t\lfloor n/2\rfloor$ triangles. The paper writes the edge count as $f(n)+t$ with $f(2m)=m^2$ and $f(2m+1)=m(m+1)$, that is $f(n)=\lfloor n^2/4\rfloor$. On p. 122 the same paper records Rademacher's unpublished case $t=1$ for even $n$, states the conjecture for $t<\lfloor n/2\rfloor$ that Problem 1010 asks about, and shows that it fails at $t=n/2$ for even $n>4$. The page's date is the issue's, 1 March 1962 (Crossref; the reprint head reads Vol. 6, No. 1, March 1962).

Covers. The question for $t<c_1n/2$, with $c_1$ not made explicit: for each fixed $t$, every $n$ large in terms of $t$. Not the range $c_1n/2\le t<\lfloor n/2\rfloor$, which Lovász and Simonovits settle.

Depends on. Nothing in this wiki; the paper's Theorem and its Lemmas 1--3 are the whole argument.

Acceptance. Refereed journal publication in the Illinois Journal of Mathematics, which is the refereed evidence. The site's label PROVED rests on Lovász and Simonovits and on Nikiforov and Khadzhiivanov, so the site's credit of the linear range to Erdős is not listed as reviewed. The proof (Lemmas 2--3 and pp. 124--127) is not examined in this corpus, and nothing here is independently reviewed.