Let the pair of natural number is x and y Then, x2−y2=63 ⇒‌‌(x−y)(x+y)=63 Case-I: ‌‌x−y=7 and x+y=9 ∴x=8 and y=1 Case-II: ‌‌x−y=3 and x+y=21 ∴x=12‌ and ‌y=9 Case-III: ‌‌x−y=1 and x+y=63 ∴x=32,y=31 Hence, the number of pairs =3[(8,1),(12,9),(32,31)]