Newbetuts

Modular Arithmetic problem: Show that $\sum_{k=1}^{99}{(x+k)^2} = y^z$ is not solvable in integers x,y,z if z>1

How do you determine number of distinct integer solutions for an equation? [duplicate]

$a^m+k=b^n$ Finite or infinite solutions?

Cubic diophantine equation

When is $\left\lfloor \frac {7^n}{2^n} \right\rfloor \bmod {2^n} \ne 0\;$?

Given prime $p$, for any integer $a$, exist integer $x,y$ such that $p\mid y^2+x^3+a$.

Finding integer solutions to $y^2=x^3-2$

Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$?

Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers

How did Letac solve $x_1^k + x_2^k + \dots +x_9^k = 0$ for $k = 1, 3, 5, 7$ in 1942?

Is 2018 special because of these properties?

Are Transitions in a Hydrogen Atom Unique

Find the number of positive integers solutions of the equation $3x+2y=37$

Finding solutions to $2^x+17=y^2$

Representations of a ternary quadratic form, modular forms of wheight 3/2 and Eisenstein series

On $1^2+2^2+\dots+24^2 = 70^2$, and $15^3+16^3+\dots+34^3 = 70^3$

$a+b=c \times d$ and $a\times b = c + d$

New posts in diophantine-equations

Solving the Diophantine Equation $ax^2 + bx + c = dy^2 + ey + f$?

How to find all rational points on the elliptic curves like $y^2=x^3-2$

Requirements for an integer root of cubic equation

Modular Arithmetic problem: Show that $\sum_{k=1}^{99}{(x+k)^2} = y^z$ is not solvable in integers x,y,z if z>1

How do you determine number of distinct integer solutions for an equation? [duplicate]

$a^m+k=b^n$ Finite or infinite solutions?

Cubic diophantine equation

When is $\left\lfloor \frac {7^n}{2^n} \right\rfloor \bmod {2^n} \ne 0\;$?

Given prime $p$, for any integer $a$, exist integer $x,y$ such that $p\mid y^2+x^3+a$.

Finding integer solutions to $y^2=x^3-2$

Congruence properties of $a^5+b^5+c^5+d^5+e^5=0$?

Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers

How did Letac solve $x_1^k + x_2^k + \dots +x_9^k = 0$ for $k = 1, 3, 5, 7$ in 1942?

Is 2018 special because of these properties?

Are Transitions in a Hydrogen Atom Unique

Find the number of positive integers solutions of the equation $3x+2y=37$

Finding solutions to $2^x+17=y^2$

Representations of a ternary quadratic form, modular forms of wheight 3/2 and Eisenstein series

On $1^2+2^2+\dots+24^2 = 70^2$, and $15^3+16^3+\dots+34^3 = 70^3$

$a+b=c \times d$ and $a\times b = c + d$