Titlebook: Elements of Number Theory; John Stillwell Textbook 2003 Springer Science+Business Media New York 2003 Euclidean algorithm.number theory.pr

Bravura

Management von NetzwerkorganisationenFermat’s remarkable discovery that odd primes of the . form . +. are in fact those of the . form 4.+ 1 led to the more general problem of describing primes of the form .+ . for nonsquare integers .. Is it true, for each ., that the primes of the form . + . are those of a finite number of linear forms?

Arteriography

Management von Open-Innovation-NetzwerkenThis chapter unites many of the algebraic structures encountered in this book—the integers, the integers mod ., and the various extensions of the integer concept by Gauss, Eisenstein and Hurwitz—in the single abstract concept of ..

PLE

Definition des Plattformkonzepts,This chapter pursues the idea that a number is known by the set of its multiples, so an “ideal number” is known by a set that . a set of multiples. Such a set . in a ring . is called an ideal, and it is defined by closure under sums (. ∈ . ⇒ . + . ∈ .) and under multiplication by all elements of the ring (. ∈ ., . ∈ . ⇒ . ∈ .).

工作

AIL

SLING

Congruence arithmetic,Many questions in arithmetic reduce to questions about remainders that can be answered in a systematic manner. For each integer . >1 there is an arithmetic “mod .” that mirrors ordinary arithmetic but is ., since it involves only the . remainders 0, 1, 2,..., .-1 occurring on division by .. Arithmetic mod ., or ., is the subject of this chapter.

Presbyopia

恸哭

Quadratic integers,Just as Gaussian integers enable the factorization of x. + ., other quadratic expressions in ordinary integer variables are factorized with the help of .. Examples in this chapter are ..

Decongestant

Judicious

Quadratic reciprocity,Fermat’s remarkable discovery that odd primes of the . form . +. are in fact those of the . form 4.+ 1 led to the more general problem of describing primes of the form .+ . for nonsquare integers .. Is it true, for each ., that the primes of the form . + . are those of a finite number of linear forms?