Regarding the paper "An elliptic K3 surface associated to Heron triangles"
Ronald van Luijk
Part (2) of the main theorem (Thm. 1.1) takes two rational numbers
sigma_0, sigma_1 > 1.
Unfortunately, the proof uses that if these are different, then the ratios
tau_i = (sigma_i-1) / ( sigma_i*(sigma_i+1) )
are different. This is clearly a false statement, as the counterexample
sigma_0 = 2 and sigma_1 = 3
shows. Indeed, for n=1, the triangles found in Remark 1.2 for these
sigma_i are similar.
One way to fix the theorem is to take sigma_i > 1 + sqrt(2).
I thank Martin Bråtelund for noting this and suggesting the fix.