Get A Life!

In his latest book, "Numbers: Their Tales, Types, and Treasures," Alfred Posamentier mentions what he labels, "Pythagorean Curiosity #4":

It seems that in the mid-1600s the ever-inquisitive Pierre de Fermat sought a Pythagorean triple wherein the SUM of the two smaller values (a + b) was a square integer, AND the largest triple (c) was also a square integer.
Well, he found one such triple:

(a) 4,565,486,027,761
(b) 1,061,652,293,520 and
(c) 4,687,298,610,289

where a + b = 5,627,138,321,281 or 2,372,159²  and c = 2,165,017² 

Mind you, of course, no computers in those days!

MOREOVER, Fermat proved that this was the smallest such Pythagorean triple! (I don't know if any more such triples have been found in the almost four centuries since?)

All of which leads me to imagine being alive in 1643 (when Fermat concocted the problem) and sayin', "YO Pierre, uhhh, GET A LIFE!"  ;-)