Tag: subtraction

The Method of Complements

Abraham Lincoln once famously said, “Everybody loves a compliment.” ¬†I suspect that if he had been a mathematician he would have loved complements, too. We’ve already seen what complements are and talked about the two most prolific: the radix complement and the diminished radix complement. Now it’s time to explore how we can leverage complements …

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Modular Subtraction Rule Proof

I’ve already¬†presented and proved the rule for modular addition, so for a sense of completeness, but mostly to satisfy my OCD, now I’ll cover the rule for modular subtraction. When doing subtraction in modular arithmetic, the rule is: If we subtract integer from integer and calculate the difference modulo , we get the same answer …

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Modular Addition Rule Proof

Addition in modular arithmetic is much simpler than it would first appear thanks to the following rule: This says that if we are adding two integers and and then calculating their sum modulo , the answer is the same as if we added modulo to modulo and then calculated that sum modulo . Note that …

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