Geodesic
Searching for Diophantine quintuples
Mihai Cipu 1   ; Tim Trudgian 2
1 Simion Stoilow Institute of Mathematics of the Romanian Academy Research unit no. 5, P.O. Box 1-764 RO-014700 Bucureşti, Romania
2 Mathematical Sciences Institute The Australian National University Canberra, Australia
Acta Arithmetica, Tome 173 (2016) no. 4, pp. 365-382 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441\cdot 10^{26}$ Diophantine quintuples.
DOI : 10.4064/aa8254-2-2016
Keywords: consider diophantine quintuples these sets positive integers product elements which perfect square conjectured there diophantine quintuples improve current estimates there cdot diophantine quintuples

Mihai Cipu  1   ; Tim Trudgian  2

1 Simion Stoilow Institute of Mathematics of the Romanian Academy Research unit no. 5, P.O. Box 1-764 RO-014700 Bucureşti, Romania
2 Mathematical Sciences Institute The Australian National University Canberra, Australia 
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Mihai Cipu; Tim Trudgian. Searching for Diophantine quintuples. Acta Arithmetica, Tome 173 (2016) no. 4, pp. 365-382. doi: 10.4064/aa8254-2-2016

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