Newbetuts

For every positive integer n there exists an odd integer m such that $2^{2n} + m$ is a perfect square.

$s(n) = a_1 p_1^n + \dots + a_k p_k^n + a_{k + 1}$ is a perfect square for every $n$, prove that $a_1 = a_2 = \dots = a_k = 0$ & $a_{k + 1}$ a square

General method for determining if $Ax^2 + Bx + C$ is square

Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$

$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $

Generalisation of this circular arrangement of numbers from $1$ to $32$ with two adjacent numbers being perfect squares

Are the square roots of all non-perfect squares irrational? [duplicate]

If $\gcd(x,y)=1$, and $x^2 + y^2$ is a perfect sixth power, then $xy$ is a multiple of $11$

Finding integer cubes that are $2$ greater than a square, $x^3 = y^2 + 2$ [duplicate]

Show that $x^2+y^2+z^2=999$ has no integer solutions

How do I prove that $3^n - 3$ is never a square number?

Proving that a list of perfect square numbers is complete

When is $ 999\cdots$ a perfect square?

If there is one perfect square in an arithmetic progression, then there are infinitely many

On the conjecture that, for every $n$, $\lfloor e^{\frac{p_{n^2}\#}{p_{n^2 + 1}}}\rfloor $ is a square number.

Olympiad problem: Erdos-Selfridge

Prove or disprove that $8c+1$ is square number.

New posts in square-numbers

Structures in the plot of the "squareness" of numbers

Finding all integers such that $a^2+4b^2 , 4a^2+b^2$ are both perfect squares

Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.

For every positive integer n there exists an odd integer m such that $2^{2n} + m$ is a perfect square.

$s(n) = a_1 p_1^n + \dots + a_k p_k^n + a_{k + 1}$ is a perfect square for every $n$, prove that $a_1 = a_2 = \dots = a_k = 0$ & $a_{k + 1}$ a square

General method for determining if $Ax^2 + Bx + C$ is square

Is $\left( {{2}^{x}}-1 \right)\left( {{5}^{x}}-1 \right)$ a square number for integer $x>1$

$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $

Generalisation of this circular arrangement of numbers from $1$ to $32$ with two adjacent numbers being perfect squares

Are the square roots of all non-perfect squares irrational? [duplicate]

If $\gcd(x,y)=1$, and $x^2 + y^2$ is a perfect sixth power, then $xy$ is a multiple of $11$

Finding integer cubes that are $2$ greater than a square, $x^3 = y^2 + 2$ [duplicate]

Show that $x^2+y^2+z^2=999$ has no integer solutions

How do I prove that $3^n - 3$ is never a square number?

Proving that a list of perfect square numbers is complete

When is $ 999\cdots$ a perfect square?

If there is one perfect square in an arithmetic progression, then there are infinitely many

On the conjecture that, for every $n$, $\lfloor e^{\frac{p_{n^2}\#}{p_{n^2 + 1}}}\rfloor $ is a square number.

Olympiad problem: Erdos-Selfridge

Prove or disprove that $8c+1$ is square number.