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Find $a,b,c,d,e$ such that $\frac{s}a+1,\frac{s}b+1,\frac{s}c+1,\frac{s}d+1,\frac{s}e+1$ are all perfect squares $ (s=abcde)$

On the arithmetic differential equation $n''=n'$

Why does the diophantine equation $x^2+x+1=7^y$ have no integer solutions?

How do I show that the sum $(a+\frac12)^n+(b+\frac12)^n$ is an integer for only finitely many $n$?

Elementary Diophantine equation

When is $2^n -7$ a perfect square?

Show $15x^{2} - 7y^{2} = 9$ has no integer solutions

Find all solutions: $x^2 + 2y^2 = z^2$

When is $1^5 + 2^5 + \ldots + n^5$ a square?

What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

Trigonometric diophantine equation $8\sin^2\left(\frac{(k+1)\pi}{n}\right)=n\sin\left(\frac{2\pi}{n}\right)$

Birational Equivalence of Diophantine Equations and Elliptic Curves

For what kind of positive integers $m+n+m^2+n^2 \mid m^3+n^3$ holds?

Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$ [closed]

How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma

New posts in diophantine-equations

Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?

A diophantine equation with only "titanic" solutions

Fermat's Last Theorem simple proof

Examples of Diophantine equations with a large finite number of solutions

For integers $a\ge b\ge 2$, is $f(a,b) = a^b + b^a$ injective?

Find $a,b,c,d,e$ such that $\frac{s}a+1,\frac{s}b+1,\frac{s}c+1,\frac{s}d+1,\frac{s}e+1$ are all perfect squares $ (s=abcde)$

On the arithmetic differential equation $n''=n'$

Why does the diophantine equation $x^2+x+1=7^y$ have no integer solutions?

How do I show that the sum $(a+\frac12)^n+(b+\frac12)^n$ is an integer for only finitely many $n$?

Elementary Diophantine equation

When is $2^n -7$ a perfect square?

Show $15x^{2} - 7y^{2} = 9$ has no integer solutions

Find all solutions: $x^2 + 2y^2 = z^2$

When is $1^5 + 2^5 + \ldots + n^5$ a square?

What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

Trigonometric diophantine equation $8\sin^2\left(\frac{(k+1)\pi}{n}\right)=n\sin\left(\frac{2\pi}{n}\right)$

Birational Equivalence of Diophantine Equations and Elliptic Curves

For what kind of positive integers $m+n+m^2+n^2 \mid m^3+n^3$ holds?

Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$ [closed]

How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma