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A complex circular intuitionistic fuzzy decision framework for evaluating sustainable agriculture strategies under uncertainty. [PDF]

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Yu Y.
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On a Diophantine Equation

Vietnam Journal of Mathematics, 2021
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Combinatorial Diophantine equations

Publicationes Mathematicae Debrecen, 2000
For a positive integer \(k\) let \(P_k(x)=x(x+1)\ldots (x+k-1)\) and \(S_k(x)=1^k+2^k+\ldots +x^k\). In the paper the following Diophantine equations are solved (or resolved): \(P_6(x)=P_4(y)\), \(P_6(x)={y\choose 2}\), \(P_6(x)={y\choose 4}\), \({x\choose 3}=P_2(y)\), \({x\choose 3}=P_4(y)\), \({x\choose 6}=P_2(y)\), \({x\choose 6}=P_4(y)\), \({x ...
Hajdu, L., Pintér, Á.
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On a diophantine equation

Mathematical Notes, 2016
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A class of Diophantine equations

Publicationes Mathematicae Debrecen, 1992
A method is given for the resolution of diophantine equations of type \(F(2^ a\cdot 3^ b)=\pm 2^ c\cdot 3^ d\), where \(F(x)\in\mathbb{Z}[x]\) has at least two distinct roots. The method is based on lower bounds for linear forms in logarithms of algebraic numbers and the LLL-lattice basis reduction algorithm.
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Aggregating diophantine equations

Zeitschrift für Operations Research, 1972
Mathews [1897] has given a theorem for aggregating two diophantine equations with positive integer coefficients into a single equation that has the same solution set as its parents over the nonnegative integers. Building on this result,Elmaghraby andWig [1970] show how to shrink the inequality constraints of a bounded variable integer program to a ...
Fred W. Glover, Robert E. D. Woolsey
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Quadratic diophantine equations

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1960
Abstract Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations.
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Diophantine Equations and Computation

2009
Unless otherwise stated, we'll work with the natural numbers : $$N = \{0,1,2,3, \dots\}.$$ Consider a Diophantine equation F (a 1 ,a 2 ,...,a n ,x 1 ,x 2 ,...,x m ) = 0 with parameters a 1 ,a 2 ,...,a n and unknowns x 1 ,x 2 ,...,x m For such a given equation, it is usual to ask: For which values of the parameters does the equation have a ...
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Universal diophantine equation

Journal of Symbolic Logic, 1982
In 1961 Martin Davis, Hilary Putnam and Julia Robinson [2] proved that every recursively enumerable set W is exponential diophantine, i.e. can be represented in the formHere P is a polynomial with integer coefficients and the variables range over positive integers.In 1970 Ju. V.
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A Class of Diophantine Equations

The Mathematical Gazette, 1938
The general solution in positive integers of the equation (1) 2 a(x 2 − y 2 ) + l = z 2 where
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