How to show that $3^x+4^x=5^x$ has only one solution?
63505
Proving that $ 2 $ is the only real solution of $ 3^x+4^x=5^x $
44247
For $a^3+b^3+c^3=3$ prove that $a^4b+b^4c+c^4a\leq3$
70147
Solving $x^4 -10x^3 + 26x^2 -10x +1 = 0$.
155743
Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
126689
Find the number of natural solutions of $5^x+7^x+11^x=6^x+8^x+9^x$
106374
Show that $2x^6+12x^5+30x^4+60x^3+80x^2+30x+45=0$ has no real roots
65000
prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
12041
Solving an equation in $x$, in which $x$ occurs as exponent four times
141371
Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
153123
Proving by induction $4^n  0$
135858
Prove $x^5 + x^4 + x^3 + x^2 + 1 = 0$ has no rational solution
106934
$x^x=y$. How to solve for $x$?
26692
Equation in integers $7^x-3^y=4$
114379
Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$