4 ms·
`251 == 0` is maths friendly because 251 is a prime number. Like the article outlines, this means that for any given number x in the field, there exists some ot
by CuriousCosmic 4y ago
`251 == 0` is maths friendly because 251 is a prime number. Like the article outlines, this means that for any given number x in the field, there exists some other y where `x * y == 1`. This isn't necessarily the case for non-primes.
When that breaks down, you can no longer invert numbers in a reversible way. aka `1/(1/x) == x` no longer holds true. This means you can no longer easily manipulate values or equations using the common set of properties established for most mathematics, hence "not maths friendly".
- deleted 4y ago[deleted]
- sbf501 4y agoSo P=256 cannot define a field because it isn't prime?
- creata 4y agoThere is a field with 256 elements, because 256 is the power of a prime. But that field is not the integers mod 256: it has different rules for addition and multiplication.
- sbf501 4y agoAh, thanks! Fields are a lot less intimidating than I thought they would be! Well, I mean: the basic idea (after reading these replies + wikipedia).
- vmilner 4y agoThere is a finite field (or Galois field GF(p)) of size p for any prime p. This can be exhibited by integers mod p. There are also finite (Galois) fields GF(p^n) of size p^n (positive integer powers of p) These can be exhibited by polynomials with coefficients in the GF(p) field with up to n terms. Eg for p = 2 and n = 3 0 1 x 1 + x 1 + x + x^2 1 + x^2 x + x^2 x^2