Results 121 to 130 of about 2,595 (231)

A remark on a Diophantine equation of S. S. Pillai

summary:S. S. Pillai proved that for a fixed positive integer $a$, the exponential Diophantine equation $x^y-y^x= a$, $\min (x,y)>1$, has only finitely many solutions in integers $x$ and $y$.
Hoque, Azizul
core   +1 more source

One Diophantine Equation

We solve a problem posed recently by J.H.E. Cohn, in proving that x = y = 1 is the only solution in nonnegative integers to the diophantine equation x^2 - 3 y^4 = -2.diophantine ...
Weger, B.M.M. de
core  

Solving Diophantine Equation Using Class Number

, 2016
Solving Diophantine Equation Using Class ...
Percival, Andrew
core  

On a diophantine equation of Andrej Dujella

, 2013
We investigate positive solutions (x,y) of the Diophantine equation x-(k+1)y=k that satisfy y < k-1, where k≥ 2.
Matthews, Keith R., Robertson, John P., White, Jim, Robertson, John, Matthews, Keith, Keith R. Matthews   +5 more
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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  

THE DIOPHANTINE EQUATION r² + r(x + y) = kxy [PDF]

, 1985
The Diophantine equation of the title is solved in ...
W R Utz
core  

The Diophantine equation x2 + 11 = 3n and a related sequence

, 1975
It is proven that the Diophantine equation x2 + 11 = 3n has as its only solution (x, n) = (4, 3). This establishes that the Diophantine equation x2 + D = pn, where D ≡ 3(mod 4) and p = (D + 1)4, is prime, has no nontrivial solutions (x, n) for D ≥ 11 ...
Alter, Ronald, Kubota, K.K.
core   +1 more source

The approximate functional equation of some Diophantine series. [PDF]

Mon Hefte Math, 2023
Chamizo F, Martin B.
europepmc   +1 more source

An inhomogeneous wave equation and non-linear Diophantine approximation

, 2008
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution.
Kristensen, S., Beresnevich, V., Dodson, M.M., Levesley, 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