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## Main Question or Discussion Point

Hello PhysicsForums!

I had been reading some examples of notions of congruence and I came across one that miffed me. I was hoping that someone could help me define this notion of congruence as described below.

If [itex]\alpha[/itex] is a quadratic integer in [itex]Q[\sqrt{-d}][/itex], a notion of congruence [itex](mod \alpha)[/itex] can be defined. Additionally, the [itex]+,-,[/itex] and [itex]x[/itex] can be defined for for congruence classes.

Can someone help me define this notion of congruence as well as the [itex]+,-,[/itex] and [itex]x[/itex] for congruence classes?

Much Thanks, --Brim

I had been reading some examples of notions of congruence and I came across one that miffed me. I was hoping that someone could help me define this notion of congruence as described below.

If [itex]\alpha[/itex] is a quadratic integer in [itex]Q[\sqrt{-d}][/itex], a notion of congruence [itex](mod \alpha)[/itex] can be defined. Additionally, the [itex]+,-,[/itex] and [itex]x[/itex] can be defined for for congruence classes.

Can someone help me define this notion of congruence as well as the [itex]+,-,[/itex] and [itex]x[/itex] for congruence classes?

Much Thanks, --Brim

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