I have to assume this is fairly common, but I'd like to know if there is a term for this technique, and what branch of mathematics it is a part of. (For reference, I have no formal training, but fell into a set of problems I need to solve, and I'm trying to understand the landscape.)

Forgive me if I'm expressing this poorly, and feel free to correct my notation and terminology:

For a set of numbers $1,2,3,4,$ where $0<n<5$

$4 + n = n$


$1 - n = 5 - n$

I understand this is analogous to a 2-bit register, and there's a problem involving reduction of symmetries in a 2^2 Latin square where this proved quite handy.

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    $\begingroup$ And could you be thinking about modular arithmetic? $\endgroup$ – Omnomnomnom Aug 24 '16 at 20:33
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    $\begingroup$ It does look like congruence modulo $4$. $\endgroup$ – Lubin Aug 24 '16 at 20:41
  • $\begingroup$ It indeed looks to be Modular arithmetic. (Gauss's name has been popping up a lot, I'm psyched to finally make the connection. Plenty of material there for me to study.) Thank you! $\endgroup$ – DukeZhou Aug 24 '16 at 20:47

To future readers: he was thinking of modular arithmetic.


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