How many pairs (m, n) of positive integers satisfy the equation $$m^2 + 105 = n^2$$?

Question

Accepted Answer

n 2 − m 2 = 105 n^2-m^2=105 n 2 − m 2 = 105 (n-m)(n+m) = 1*105, 3*35, 5*21, 7*15, 15*7, 21*5, 35*3, 105*1. n-m=1, n+m=105 ==> n=53, m=52 n-m=3, n+m=35 ==> n=19, m=16 n-m=5, n+m=21 ==> n=13, m=8 n-m=7, n+m=15 ==> n=11, m=4 n-m=15, n+m=7 ==> n=11, m=-4 n-m=21, n+m=5 ==> n=13, m=-8 n-

How many pairs (m, n) of positive integers satisfy the equation m2+105=n2m^2 + 105 = n^2m2+105=n2?

How many pairs (m, n) of positive integers satisfy the equation $m^2 + 105 = n^2$ ?