Category Archives: modular arithmetic

Post without words #26

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Chinese Remainder Theorem proof

In my previous post I stated the Chinese Remainder Theorem, which says that if and are relatively prime, then the function is a bijection between the set and the set of pairs (remember that the notation means the set ). … Continue reading

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More words about PWW #25: The Chinese Remainder Theorem

In a previous post I made images like this: And then in the next post I explained how I made the images: starting in the upper left corner of a grid, put consecutive numbers along a diagonal line, wrapping around … Continue reading

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A few words about PWW #25

In my previous post I made images like this: What’s going on? Well, first, it’s easy to notice that each grid starts with in the upper-left square; is one square down and to the right of , then is one … Continue reading

Posted in modular arithmetic, number theory, posts without words | Tagged , , , , | 4 Comments

Post without words #25

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Finding the repetend length of a decimal expansion

We’re still trying to find the prefix length and repetend length of the decimal expansion of a fraction , that is, the length of the part before it starts repeating, and the length of the repeating part. In my previous … Continue reading

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MaBloWriMo 24: Bezout’s identity

A few days ago we made use of Bézout’s Identity, which states that if and have a greatest common divisor , then there exist integers and such that . For completeness, let’s prove it. Consider the set of all linear … Continue reading

Posted in algebra, arithmetic, modular arithmetic, number theory | Tagged , , , , , , , | 2 Comments