Question

if 2013 + a² = b². find a*b ?

Answer 1

2013=b^2-a^2

2013 =(b-a)(b+a)

(b-a)(b+a)=3*11*61
doing prime factorisation

(b-a)(b+a)=33×61

b-a=33---(1)

b+a=61----(2)

add both (1) and (2)

2b=94

b=94/2
b=47
substitute b value in (2)

47+a=94

a=94-47
a=44

therefore
a*b = 44*47
=2068