On p.4 you argue that for integers a, b, c and n:
(a + b − c)^n = (c − a)(c − b)g_1(n)
=> a + b − c = [(c − a)(c − b)g_1(n)]^(1/n)
=> g_1(n) | a + b - c
This doesn't follow as it stands. For example, if a=b=3 and c=n=2, then g_1(n)=16 whereas a + b - c = 4.