Indeed, the Galois group of " K " / " Q " is abelian and can be canonically identified with the group of invertible residue classes mod " N ".
22.
Where ? denotes the signature of a permutation and ? " a " is the permutation of the nonzero residue classes mod " p " induced by multiplication by " a ".
23.
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 ):
24.
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 ):
25.
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 }.
26.
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.
27.
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.
28.
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.
29.
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.
30.
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.
