Results 81 to 90 of about 1,143,114 (202)
Open Computer Science, 2018 We define a computable function f from positive integers to positive integers. We formulate a hypothesis which states that if a system S of equations of the forms xi· xj = xk and xi + 1 = xi has only finitely many solutions in non-negative integers x1, .
Tyszka Apoloniusz
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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The matrix diophantine equations $AX + BY = C$
Karpatsʹkì Matematičnì Publìkacìï, 2013 A method of constructing of solutions of matrix Diophantine equations $AX + BY = C$ over commutative domains of finitely generated principal ideals is suggested. The formulas of general solutions of such equations in some cases is proposed. The criterion
N. S. Dzhaliuk, V. M. Petrychkovych
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Diophantine equations in separated variables and polynomial power sums. [PDF]
Mon Hefte Math, 2021 Fuchs C, Heintze S.
europepmc +1 more source
On a Diophantine Equation of Stroeker
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2010 The authors prove that there are infinitely many positive integers \(N\) such that the Diophantine equation \((x^2+y)(x+y^2)=N(x-y)^3\) has no nontrivial integer solution \((x,y)\).
Luca, Florian +2 more
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The diophantine equation r2+r(x+y)=kxy
International Journal of Mathematics and Mathematical Sciences, 1985 The Diophantine equation of the title is solved in integers.
W. R. Utz
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Separable Diophantine equations [PDF]
Transactions of the American Mathematical Society, 1945 Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
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An exponential diophantine equation [PDF]
Bulletin of the Australian Mathematical Society, 2001 Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
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Diophantine Solutions Based Permutation for Image Encryption
Journal of Algorithms & Computational Technology, 2013 A permutation technique based on the resolution of the system of three independent Diophantine equations is presented. Each Diophantine equation parameters are two positive integers generated from a chaotic system.
J. S. Armand Eyebe Fouda +3 more
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, 1979 Includes bibliographical references (page 33)An equation which contains two or more variables and satisfied\ud by an infinite number of values for each of the unknowns is called\ud indeterminate or diophantine, after Diophantus of Alexandria (250 A.D ...
Archibald, Janet Susan
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