find all integers $a,b,c$ such that $a^2=bc+1,$ $b^2=ca+1.$
79
Find $a$, $b$ and $c$ that satisfy the following equations
52658
What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
153053
Find numbers $a, b, c$ given that $a+b+c=12$, $a^2+b^2+c^2=50$, and $a^3+b^3+c^3=168$
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
47737
Find all the possible values of $(a,b,c,d)$.
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
100761
Find all $x$ such that $x^6 = (x+1)^6$.
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
81226
Find all integers $a$ for which $x^2-x+a$ divide $x^{13}+x+90$.
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
40447
Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$