Abstract
We search for three distinct polynomials with integer coefficients such that the product of any two members of the set added with their sum and increased by a non-zero integer (or polynomial with integer coefficients) is a perfect square.
Highlights
The problem of constructing the set with property that the product of any two its distinct elements is one less than a square has a very long history and such sets were studied by Diophantus.A set of m positive integers is called a Diophantine m-tuple if is a perfect square (1)a perfect square for all
Many mathematicians consider the problem of the existence of Diophantine quadruples with the property D(n) for any arbitrary integer n and for any linear polynomials in n
On solving equation, (20) and (21), we get Assuming The initial solution of equation (17) is given by in (22), it reduces to is a perfect
Summary
A set of m positive integers is called a Diophantine m-tuple if is a perfect square Many mathematicians consider the problem of the existence of Diophantine quadruples with the property D(n) for any arbitrary integer n and for any linear polynomials in n. The above results motivated us the following definition: A set of three distinct polynomials with integer coefficient is said to be a special dio 3- tuple with property D(n) if is a perfect square for all
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