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Title |
Some polynomial formula of the Diophantine Quadruple with D(n) property |
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Author |
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 |
| Citation |
Vol. 19 No. 4 pp. 249-251 |
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Abstract |
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. |
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Keywords |
diophantine quadruple ,arithmeticprogression, diophantine m-tuple |
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