Diophantine equations are polynomial equations $F=0$, or systems of polynomial equations $F_1=\ldots=F_k=0$, where $F,F_1,\ldots,F_k$ are polynomials in either $\mathbb{Z}[X_1,\ldots,X_n]$ of $\mathbb{Q}[X_1,\ldots,X_n]$ of which it is asked to find solutions over $\mathbb{Z}$ or $\mathbb{Q}$. ...

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### Linear diophantine quasivariety having a unique solution

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**1**answer

### Does $2^x-3p^y=5$ (with $p$ an odd prime) have only finitely many positive integer solutions?

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**1**answer

### Number of integer solutions of a linear equation under constraints

**7**

**1**answer

### Rational perfect power values of $y(y+1)$

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### Hyperelliptic curves imply FLT-like results

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### No rational points on $x^n+a=y^2$ for all $n>4$"?

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### On $x^4+16z^n=y^2$ and $x^4+z^n=y^2$

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### A specific Diophantine equation restricted to prime values of variables.

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**1**answer

### Solving elliptic equation in rational functions

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### Solving a quadratic diophantine - writing sum of four squares with three parameters

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**1**answer

### What is the time complexity for solving Diophantine equations of degree 2?

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### A generalization of Bernoulli's inequality and what does it application for?

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### On the diophantine equations $x^n+n=y^m$ and $x^n-n=y^m$

**7**

**1**answer

### $(2x^2+1)(2y^2+1)=4z^2+1$ has no positive integer solutions?

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**1**answer

### Solutions to linear equations from recurrence sequences with no repeated roots

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### Isomorphism classes of lattices

**6**

**4**answers

### Solutions to the Diophantine equation $x^2+3y^2+3z^2=n$

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**1**answer

### On the Diophantine equation $x^{4}+y^{4}=z^p$

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**1**answer

### Does Fermat's last theorem hold in the Grothendieck ring of the ordinals?

**9**

**1**answer

### Enquiry on a Diophantine problem

**3**

**1**answer

### Density version of the Erdos-Graham conjecture

**4**

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### Number of nontrivial integral solutions to $f(x)=f(y)$

**0**

**0**answers

### Solutions to exponential diophantine: 2^a + 3^b = 2^c + 3^d [duplicate]

**2**

**0**answers

### Can we efficiently factor $n$ given that $n=pq$ where $p,q$ are primes satisfying $p=a^2+b^2, q=2ab+1$ for some $a,b$

**1**

**1**answer

### Dimension of $S$-units over $\mathbb{C}[x]$

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### Does each integer have the form $x^4-y^3+z^2$ with $x,y,z$ positive integers?

**3**

**1**answer

### Solution to an exponential Diophantine equation

**5**

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### Is every integer $n>1$ the sum of two triangular numbers and two powers of $5$?

**14**

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### Does every integer $n>1$ have the form $a^2+b^2+3^c+5^d$ with $a,b,c,d$ nonnegative integers?

**0**

**0**answers

### Mathematical Aspects of Hectoc-type Puzzles

**4**

**1**answer

### Solutions to diophantine equation

**3**

**1**answer

### Diophantine equations and 'quasi-paucity'

**2**

**0**answers

### Full-rank factorization property of integer-valued matrices

**10**

**0**answers

### Is every integer a difference of two powers?

**11**

**1**answer

### Infinitely many integer solutions to $X^4+Y^4-18Z^4= -16$

**0**

**0**answers

### On existence of certain primes and integers

**3**

**1**answer

### What is known about equation $a^{n+k}+b^{n+l}=c^{n+m}$ and its set of solutions?

**6**

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### Solve this Diophantine equations $(2^x-1)(3^y-1)=2z^2$

**8**

**2**answers

### How are such sets of natural numbers called?

**8**

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### Product of four consecutive primes plus $1$ equals square

**2**

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### Genus Zero Diophantine Equations and Infinite Valuations

**0**

**6**answers

### If $n=x^k+y^k$ then also $n=a^2+b^2=c^3+d^3=\ldots =x^k+y^k$ [closed]

**0**

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### Could a full rank linear system arise from this construction?

**2**

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### minimum size of undecidable quadratic diophantine problems

**15**

**3**answers

### Number of solutions to polynomial congruences

**2**

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### Bound for the number of solutions to a system of congruence relations

**8**

**1**answer

### Integral complete 4-partite graphs

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### Tripathi's formulas for Frobenius number in three variables

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### Existence of certain diophantine equations

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**2**answers