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# Category Archives: modular arithmetic

## 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

## 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

Posted in modular arithmetic, number theory, posts without words
Tagged Chinese, grid, remainder, theorem, torus
2 Comments

## 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 Chinese, grid, remainder, theorem, torus
4 Comments

## 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

Posted in computation, group theory, modular arithmetic, number theory, pattern
Tagged decimal, expansion, group theory, rational, repeating, repetend, totient

## 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 Bezout, combination, divisor, gcd, identity, linear, MaBloWriMo, proof
2 Comments