Results 101 to 110 of about 1,224,172 (204)

On Some Diophantine Equations

, 1988
Our purpose is to study a variety of Diophantine equations involving the Smarandache function.
Tuţescu, Lucian, Burton, Emil
openaire   +2 more sources

All solutions of consecutive natural numbers sum equation and their closed forms

Al-Jabar
Purpose: This study aims to find a closed-form solution for all ordered pairs of natural numbers (?,?) satisfying the consecutive natural number sum equation 1 + 2 + ⋯ + ? sama dengan (? + 1) + (? + 2) + ⋯ + ?. This research contributes to number theory,
Sofihara Al Hazmy, Cahya Alkahfi, Muhamad Syazali, Fulkan Kafilah Al Husein   +3 more
doaj   +1 more source

On the Diophantine equation x3=dy2±q6

International Journal of Mathematics and Mathematical Sciences, 2001
Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this paper, we have proved that if (x,q)=1, then x3=dy2±q6 has exactly two solutions provided q≢±1(mod24).
Fadwa S. Abu Muriefah
doaj   +1 more source

Exponential Diophantine equations [PDF]

Pacific Journal of Mathematics, 1982
Brenner, J. L., Foster, Lorraine L.
openaire   +3 more sources

Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

Open Computer Science, 2017
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
doaj   +1 more source

Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$

, 2005
summary:In this paper the special diophantine equation $\frac{q^{n}-1}{q-1}=y$ with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of $y-1$
Polický, Zdeněk
core   +1 more source

关于方程x²-1=yⁿ

四川大学学报. 自然科学版, 1962
Recently, Chao Koc 1 3' E2:i proved that the diophantine equationshave no integral solutions x,y with xy dpO..n this paper, I shall prove that the diophantine equation is impossible when p = 5, 7, 11, 13, 17, 19, 23, 29, 41, 43, 47,.> -r. 53, 61, 71, 79,
张世勋
doaj  

On a Diophantine equation of Erdös

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994
The second lemma is not proved in the quoted paper. It would lead to a polynomial bound in the height of the binary form. Despite this the main results can be true.
openaire   +3 more sources

On a quartic diophantine equation

, 1996
In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91.
Weger, de, B.M.M., de Weger, BMM (Frederike), Stroeker, RJ (Roel), Stroeker, R.J.   +3 more
core   +1 more source

关于丢番都方程x^xy^y=z^z

四川大学学报. 自然科学版, 1958
柯召于“Note on the Diophantine equation xxyy=zz”（见Chinese Math.Journal1940）中证明了 ...
A.Schinzel
doaj