no. of positive integral solution of x^4 - y^4 = 3789108

a) 0

b) 1

c) 2

d) 4

Both x and y are even or both x and y are odd (i.e. x and y are of the same parity)

If, both x and y are odd, then since every odd square is of the form 8k+1, LHS is divisible by 8, whereas RHS is not.

If both x and y are even, then LHS is divisible by 16, whereas we have already seen that RHS is not divisible by 8 and hence not divisible by 16 too.