I'm having trouble understanding the proof for 2 being a quadratic residue mod p <=> p = plus or minus 1 mod 8. I'm using the Springer Elementary Number Theory text. For (=>), the text says (p^2-1)/8 is even <=> 16 divides (p^2-1) <=> 16 divides (p+1)(p-1) <=> 8 divides (p+1) or 8 divides (p-1). My trouble is with this last line. I know I'm missing something obvious, but I don't see how 16 divides (p+1)(p-1) <=> 8 divides (p+1) or 8 divides (p-1). Can anyone help?