Visible Structures in Number Theory
Notes on the representations
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- Digits - the digits of the base b representation of the number.
- Continued Fraction - The simple continued fraction of a number x is a list that has as its first entry [x], the integer part of x. The list ends right there if x is an integer; and if not, the rest of the list is the simple continued fraction representation of 1/(x-[x]). For examples, see a related webMathematica page. Right now, the continued fraction representations of some numbers get truncated. I think it's a restriction on this account, but I'm not sure.
- Integer parts of multiples - A fairly simple idea: take the integer parts of the multiples x, 2x, 3x, ...; and then reduce mod m. Do these sequences uniquely characterize x?
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