212 Pythagorean triples
6.3 Lewis Carroll’s conjecture on triples of equiareal
Pythagorean triangles
Lewis Carroll conjectured that there is an infinity of Pythagorean trian-
gles with equal areas. If(p, q, r)satisfyp^2 +pq+q^2 =r^2 , then the
Pythagorean triangles generated by(r, p),(r, q), and(p+q, r)have the
same areapqr(p+q). Since there is an infinity of such triangles, there
conjecture is established. This is essentially in Diophantus.