Nim multiplication.
Reduced bases for lattices and factorization of polynomials
Generating units modulo an odd integer by addition and subtraction
Approximatting rings of integers in number fields
In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be well-solved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients. Such fields occur in the number field sieve algorithm for factoring integers. Applying a variant of a standard algorithm for finding rings of integers, one finds a subring of the number field...
Primality testing algorithms
Artin's conjecture on primes with prescribed primitive roots
Perfect arithmetic codes
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