TY - JOUR
T1 - The sum of irreducible fractions with consecutive denominators is never an integer in PA-
AU - Pambuccian, Victor
PY - 2008
Y1 - 2008
N2 - Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums Σik=1 mi/n+i (with k ≥ 1, (mi,n + i) = 1, mi < n + i) and Σik=0 1/m+in (with n, m, k positive integers) are never integers, are shown to hold in PA-, a very weak arithmetic, whose axiom system has no induction axiom.
AB - Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums Σik=1 mi/n+i (with k ≥ 1, (mi,n + i) = 1, mi < n + i) and Σik=0 1/m+in (with n, m, k positive integers) are never integers, are shown to hold in PA-, a very weak arithmetic, whose axiom system has no induction axiom.
KW - Kaye's PA
KW - Kürschák's theorem
KW - Nagell's theorem
KW - Weak arithmetic
UR - http://www.scopus.com/inward/record.url?scp=84875514235&partnerID=8YFLogxK
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U2 - 10.1215/00294527-2008-021
DO - 10.1215/00294527-2008-021
M3 - Article
AN - SCOPUS:84875514235
SN - 0029-4527
VL - 49
SP - 425
EP - 429
JO - Notre Dame Journal of Formal Logic
JF - Notre Dame Journal of Formal Logic
IS - 4
ER -