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Some polynomial formula of the Diophantine Quadruple with D(n) property


Abdul Hakeem Phulpoto, Israr Ahmed, Inayatullah Soomro, Abdul Hameed, Raza Muhammed, Imdad Ali jokhio, Rozina chohan, Abdul Naeem Kalhoro, Shah Nawaz Phulpoto, Ali Dino Jumani


Vol. 19  No. 4  pp. 249-251


The original problem of quadruple was studied by the Since the Greek mathematician Diophantus of Alexandria 1/16 , 33/16 ,17/4 and 105/16 was the first set of quadruples found in 3^rd century (b.c) in which having any product of two terms increasing the set increased by 1 is a perfect square. Later Fermat obtained a set from integers as {1,3,8,120}, later davenport and baker both to generalize the fourth member of the set is, {1,3,8, d}. Here in this work we will present a more generalized version of Diophantine quadruple, {p, q, r, s}, where any two of the product increased by n result will be a perfect square, i.e. pq+n=x^2 and, It is proved that the Diophantine quadruple , set of positive and negative integer number with the property that the product of any two of them plus n is a perfect square, than generalization of the result is obtained.


diophantine quadruple ,arithmeticprogression, diophantine m-tuple