Will there always be integer solutions for $x$ and $y$ in $3^y = 2^x - 1$?
7279
$|2^x-3^y|=1$ has only three natural pairs as solutions
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
139017
If a polynomial takes integer values at every integer, does it have integer coefficients?
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
158933
Rational solutions of $y^2 = x^3 - x$
155757
Number theory: $x^y + 1 = y^x$
87029
Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$
55437
When does $2^{n}$ divide $3^{n}-1$
3621
How can I show that $y'=\sqrt{|y|}$ has infinitely many solutions?
130565
Find all solutions to $x^3+(x+1)^3+ \dots + (x+15)^3=y^3$
75957
Prove $x^3+3y^3+9z^3-9xyz=1$ has infinity integers solutions!
46668
How to find integer solutions to $M^2=5N^2+2N+1$?
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$
151692
When does $2^n-1$ divide $3^n-1$?
99264
the number of positive-integer solutions that satisfy $x_1\cdot x_2\cdot x_3\cdot x_4=1,000,000$?