True or False—Every Baudhāyana triple is either a primitive triple or a scaled version of a primitive triple.
True. Every Baudhāyana triple is either primitive (having no common factor greater than 1) or can be reduced to a primitive triple by dividing all three numbers by their greatest common divisor (GCD). For example, (9, 12, 15) is not primitive but is a scaled version of (3, 4, 5) with scale factor 3. Conversely, any primitive triple multiplied by a positive integer gives a valid Baudhāyana triple.
Explanation
The chapter defines primitive Baudhāyana triples as those with no common factor greater than 1, and shows that if (a, b, c) is a Baudhāyana triple, then (ka, kb, kc) is also a Baudhāyana triple for any positive integer k. The converse is also true: any non-primitive triple (a, b, c) with common factor f can be reduced to (a/f, b/f, c/f), which is a primitive Baudhāyana triple. This establishes a one-to-one correspondence between all Baudhāyana triples and primitive triples with scaling factors.