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## Displaying 1 – 20 of 314

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### 14-term arithmetic progressions on quartic elliptic curves.

Journal of Integer Sequences [electronic only]

### A class of diophantine equations connected with certain elliptic curves over $Q\left(\sqrt{-13}\right)$

Compositio Mathematica

### A Classical Diophantine Problem and Modular Forms of Weight 3/2.

Inventiones mathematicae

### A diophantine system.

International Journal of Mathematics and Mathematical Sciences

### A New Characterization of the Integer 5906.

Manuscripta mathematica

### A note on integral clock triangles.

Annales Mathematicae et Informaticae

### A note on Sierpiński's problem related to triangular numbers

Colloquium Mathematicae

We show that the system of equations ${t}_{x}+{t}_{y}={t}_{p},{t}_{y}+{t}_{z}={t}_{q},{t}_{x}+{t}_{z}={t}_{r}$, where ${t}_{x}=x\left(x+1\right)/2$ is a triangular number, has infinitely many solutions in integers. Moreover, we show that this system has a rational three-parameter solution. Using this result we show that the system ${t}_{x}+{t}_{y}={t}_{p},{t}_{y}+{t}_{z}={t}_{q},{t}_{x}+{t}_{z}={t}_{r},{t}_{x}+{t}_{y}+{t}_{z}={t}_{s}$ has infinitely many rational two-parameter solutions.

Acta Arithmetica

### A note on the diophantine equation $\left({x}^{2}-1\right)\left({y}^{2}-1\right)={\left({z}^{2}-1\right)}^{2}$

Colloquium Mathematicae

### A note on the integer solutions ofhyperelliptic equations

Colloquium Mathematicae

Acta Arithmetica

Acta Arithmetica

### A remark on prime divisors of lengths of sides of Heron triangles.

Experimental Mathematics

### A solution to an “unsolved problem in number theory”.

Southwest Journal of Pure and Applied Mathematics [electronic only]

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

### An elliptic curve having large integral points

Czechoslovak Mathematical Journal

The main purpose of this paper is to prove that the elliptic curve $E:{y}^{2}={x}^{3}+27x-62$ has only the integral points $\left(x,y\right)=\left(2,0\right)$ and $\left(28844402,±154914585540\right)$, using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.

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