000091341 001 __ 91341
000091341 005 __20141007154704.0
000091341 024 8_ $9 artpubuab $9 driver $a oai:ddd.uab.cat:91341
000091341 024 7_ $2 doi $a 10.5565/PUBLMAT_56212_07
000091341 035 __ $9 articleid $a 02141493v56n2p413
000091341 041 __ $a eng
000091341 100 __ $a Drungilas, P.
000091341 245 1_ $a A degree problem for two algebraic numbers and their sum
000091341 520 3_ $a For all but one positive integer triplet (a; b; c) with a < b < c and b < 6, we decide whether there are algebraic numbers  α,β and γ  of degrees a, b and y, respectively, such that  α+β+γ = 0. The undecided case (6; 6; 8) will be included in another paper. These results imply, for example, that the sum of two algebraic numbers of degree 6 can be of degree 15 but cannot be of degree 10. We also show that if a positive integer triplet (a; b; c) satisfies a certain triangle-like inequality with respect to every prime number then there exist algebraic numbers  α,β γ of degrees a, b, c such that α+β+γ = 0. We also solve a similar problem for all (a; b; c) with a < b < c and b <6  by finding for which a, b, c there exist number fields of degrees a and b such that their compositum has degree c. Further, we have some results on the multiplicative version of the  first problem, asking for which triplets (a; b; c) there are algebraic numbers and α, β and γ  of degrees a, b and c, respectively, such that αβγ  = 1.
000091341 540 __ $9 info:eu-repo/semantics/restrictedAccess $a Tots els drets reservats $u http://www.europeana.eu/rights/rr-f/
000091341 546 __ $a Anglès
000091341 599 __ $a recerca
000091341 653 1_ $a Algebraic number
000091341 653 1_ $a Sum-feasible
000091341 653 1_ $a Abc degree problem
000091341 655 _4 $a info:eu-repo/semantics/article
000091341 655 _4 $a info:eu-repo/semantics/publishedVersion
000091341 700 __ $a Dubickas, A.
000091341 700 __ $a Smyth, C.
000091341 773 __ $g Vol. 56, Núm. 2 (2012), p. 413-448 $t Publicacions matemàtiques $x 0214-1493
000091341 856 40 $p 36 $s 452090 $u http://ddd.uab.cat/pub/pubmat/pubmat_a2012v56n2/pubmat_a2012v56n2p413.pdf
000091341 973 __ $f 0413 $l 448 $m  $n 2 $v 56 $x pubmat_a2012v56n2 $y 2012
000091341 980 __ $a ARTPUB $b PUBMAT $b UAB