D(4)-pair {;k-2, k+2}; and its extension (CROSBI ID 599508)
Prilog sa skupa u časopisu | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Filipin, Alan ; Baćić, Ljubica
engleski
D(4)-pair {;k-2, k+2}; and its extension
We prove that if k>=3, c and d are positive integers with c < d and the set {;k−2, k+2, c, d}; has the property that the product of any of its distinct elements increased by 4 is a perfect square, then d is uniquely determined. In the proof we use the standard methods used in solving similar problems. Namely, we firstly transform our problem into solving the system of simultaneous pellian equations which furthermore leads to finding intersection of binary recurrence sequences. We get the lower bound for solutions using mostly the congruence method. Combining it with hypergeometric method in which we give an improvement of known results in our special case we get the desired result for “large” values of parameter k. The remaining values of k are solved using Bakerʼs theory of linear form in logarithms.
Diophantine tuples; simultaneous Diophantine equations; linear forms in logarithms
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Podaci o prilogu
31-38.
2013.
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objavljeno
Podaci o matičnoj publikaciji
Electronic notes in discrete mathematics
Elsevier
1571-0653
Podaci o skupu
Erdös Centennial
poster
01.07.2013-05.07.2013
Budimpešta, Mađarska