Proof that a^a + b^b = c^c has no solutions for any natural numbers
87267
Conjecture similar to Fermat's Theorem.
125057
How do I solve a problem with term $a^{n} + b^{n}$?
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
111295
Prove that $a^7 + b^7 + c^7 \geq a^4b^3 + b^4c^3 + c^4a^3$
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
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
20834
Integer solutions to $c=a^2-b^2$
23835
Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
31173
How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers?
137015
Solutions for $a^2+b^2+c^2=d^2$
19945
For complex numbers $a,b,c$, explain why $a^{b\cdot c}=(a^b)^c$ is not necessarily true.