Triads of integers with equal sums of squares and equal products and a related multigrade chain
Acta Arithmetica, Tome 178 (2017) no. 1, pp. 87-100
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
While the complete solution of the problem of finding two triads of integers with equal sums of squares and equal products is known, till now no examples of three such triads has been published. In this paper we find several triads of positive integers with equal sums of squares and equal products. We present several parametric solutions for three such triads and give numerical examples for five triads of integers with equal sums of squares and equal products. We use these triads to produce multigrade chains of quadruples of integers with equal sums of $k$th powers for $k=1,2,3,5$. We conclude the paper with some open problems concerning such triads.
Keywords:
while complete solution problem finding triads integers equal sums squares equal products known examples three triads has published paper several triads positive integers equal sums squares equal products present several parametric solutions three triads numerical examples five triads integers equal sums squares equal products these triads produce multigrade chains quadruples integers equal sums kth powers conclude paper problems concerning triads
Affiliations des auteurs :
Ajai Choudhry 1 ; Jarosław Wróblewski 2
@article{10_4064_aa8574_9_2016,
author = {Ajai Choudhry and Jaros{\l}aw Wr\'oblewski},
title = {Triads of integers with equal sums of squares and equal products and a related multigrade chain},
journal = {Acta Arithmetica},
pages = {87--100},
publisher = {mathdoc},
volume = {178},
number = {1},
year = {2017},
doi = {10.4064/aa8574-9-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8574-9-2016/}
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TY - JOUR AU - Ajai Choudhry AU - Jarosław Wróblewski TI - Triads of integers with equal sums of squares and equal products and a related multigrade chain JO - Acta Arithmetica PY - 2017 SP - 87 EP - 100 VL - 178 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8574-9-2016/ DO - 10.4064/aa8574-9-2016 LA - en ID - 10_4064_aa8574_9_2016 ER -
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Ajai Choudhry; Jarosław Wróblewski. Triads of integers with equal sums of squares and equal products and a related multigrade chain. Acta Arithmetica, Tome 178 (2017) no. 1, pp. 87-100. doi: 10.4064/aa8574-9-2016
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