222 Pythagorean triples
Project: Two pairs of primitive Pythagorean triples with almost
equal perimeters
In a class in Number Theory the professor gave four students the assign-
ment of finding a fairly large primitive Pythagorean triangle using the
well known formula for the legs:
A=2mn, B=m^2 −n^2 ,C=m^2 +n^2 ,wheremandnare coprime integers, not both odd. The four students
produced four entirely different primitive triangles, but on comparing
them it was found that two of them had the same perimeter, while the
other two also had the same perimeter, this perimeter differing from the
first one by 2. This interested the class greatly, and much time was spent
in an effort to find other such sets, only to discover that there were only
four such sets with perimeters less than 500,000. Can you find at least
one such set?
perimeter m+n 2 m m n a b c
117390 273
301
117392 253
319
313038 459
527
313040 455
559
339150 425
475
525
339152 451
517
371448 469
603
371450 437
475
575