residue class वाक्य
उदाहरण वाक्य
मोबाइल
- Indeed, the Galois group of " K " / " Q " is abelian and can be canonically identified with the group of invertible residue classes mod " N ".
- Where ? denotes the signature of a permutation and ? " a " is the permutation of the nonzero residue classes mod " p " induced by multiplication by " a ".
- The norm of \ mathfrak { p } is defined as the cardinality of the residue class ring ( note that since \ mathfrak { p } is prime the residue class ring is a finite field ):
- The norm of \ mathfrak { p } is defined as the cardinality of the residue class ring ( note that since \ mathfrak { p } is prime the residue class ring is a finite field ):
- However, the twelve equal-tempered pitch classes can be represented by the cyclic group of order twelve, or equivalently, the residue classes modulo twelve, \ mathbb { Z } / 12 \ mathbb { Z }.
- For example, if, then the sum of the residue classes } } and } } is computed by finding the integer sum, then determining, the integer between 0 and 16 whose difference with 22 is a multiple of 17.
- Dirichlet's theorem on primes in arithmetic progressions shows that there are an infinity of primes in each co-prime residue class, and the prime number theorem for arithmetic progressions shows that the primes are asymptotically equidistributed among the residue classes.
- Dirichlet's theorem on primes in arithmetic progressions shows that there are an infinity of primes in each co-prime residue class, and the prime number theorem for arithmetic progressions shows that the primes are asymptotically equidistributed among the residue classes.
- The congruence classes of the integers modulo were traditionally known as " residue classes ", reflecting the fact that all the elements of a congruence class have the same remainder ( i . e ., " residue " ) upon being divided by.
- If we partitioned the even numbers into residue classes modulo 510510 instead of your modulo 6, then some of the classes not divisible by 3 would be expected to " on average " give more solutions than some of the classes divisible by 3.
- The larger sieve is applied with the set \ mathcal { S } above defined to be the set of primes for which many residue classes are removed, while the large sieve is used to obtain information using the primes outside \ mathcal { S }.
- And for each fixed residue class modulo 4, the 24 bit word, whose 1s correspond to the coordinates " i " such that " a " " i " belongs to this residue class, is a word in the binary Golay code.
- And for each fixed residue class modulo 4, the 24 bit word, whose 1s correspond to the coordinates " i " such that " a " " i " belongs to this residue class, is a word in the binary Golay code.
- A simple case is that seen in the Gauss lemma on quadratic residues, which in effect computes the transfer for the multiplicative group of non-zero residue classes modulo a prime number " p ", with respect to the subgroup { 1, & minus; 1 }.
- To prove ( i ), first note that we can compute g ( k ) either directly, i . e . by plugging in ( the residue class of ) k and performing arithmetic in \ textstyle \ mathbb { Z } / p, or by reducing f ( k ) \ mod p.
- Tate's algorithm can be greatly simplified if the characteristic of the residue class field is not 2 or 3; in this case the type and " c " and " f " can be read off from the valuations of " j " and ? ( defined below ).
- Both of the proofs ( for prime moduli ) below make use of the fact that the residue classes modulo a prime number are a Lagrange's theorem, which states that in any field a polynomial of degree " n " has at most " n " roots, is needed for both proofs.
- The splitting invariant of a prime " p " not dividing " N " is simply its residue class because the number of distinct primes into which " p " splits is ? ( " N " ) / m, where m is multiplicative order of " p " modulo " N; " hence by the Chebotarev density theorem, primes are asymptotically uniformly distributed among different residue classes coprime to " N ".
- The splitting invariant of a prime " p " not dividing " N " is simply its residue class because the number of distinct primes into which " p " splits is ? ( " N " ) / m, where m is multiplicative order of " p " modulo " N; " hence by the Chebotarev density theorem, primes are asymptotically uniformly distributed among different residue classes coprime to " N ".
- If we then lift ( mod 3 ) then we get two or four cases ( depending on whether either of " m " or " d " can be congruent to zero ( mod 3 ) ), and using the Chinese remainder theorem to glue these cases to the cases derived from " n " ( mod 16 ), we end up with four or eight cases-- some from residue classes ( mod 12 ) and some from residue classes ( mod 24 ) .)
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