Triangles with Integer Area and Integer Sides in Arithmetical Sequence/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$126$

Mistake

[$126$ is] the area of the third-smallest triangle with integral sides in arithmetical sequence and integral area: the sides are $15, 28, 41$. The first two are $3, 4, 5$ and $13, 14, 15$; the next is $15, 26, 37$, with area $156$.

Exactly what this statement is supposed to say is not clear, but the triangle with integral sides $6, 8, 10$, in arithmetic sequence, has area $24$, which is smaller than the $13, 14, 15$ triangle.

Sources

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $126$