I'm trying to understand the Proposition 5.1.1 - Ireland and Rosen, A Classical Introduction to Modern Number Theory, p.50, however, I can't understand why this argument is true: $1$ is the only quadratic residue mod $8$. I wrote a program to generate all quadratic residue modulo $8$, from $0$ to $7$
0 -> 0 1 -> 1 4 -> 4 9 -> 1 16 -> 0 25 -> 1 36 -> 4 Press any key to continue . . .
I saw $4$ there, so how come only $1$ satisfied?
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Thank you,
@Bill Dubuque: Thank you for the reference.