Question

Find the all integers a, b, c such that

a² = bc + 4, b² = ca + 4

Answer 1

a² = bc + 4 ……………. (I)

b² = 4c + 4 ……………….(ii)

Adding (i) and (ii)

a² + b² = c(a + b) + 8

subtracting(i) and (ii)

a² – b² = c(b – a)

(a – b) (a + b + c) = 0 …………….(iii)

Case I a = b

=> a² - ac - 4 = 0

D = c² + 16 = I² 

I² - c² = 16

c = 0, ± 3

Total number of solution = 12