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An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is "no", and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distinct primes is a counterexample. My question is: Are there more counterexamples?

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)=1$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is "no", and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distinct primes is a counterexample. My question is: Are there more counterexamples?

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is not and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distance prime is a countered example. My question is: Are there more countered examples?

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is "no", and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distinct primes is a counterexample. My question is: Are there more counterexamples?

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is not and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distance prime is a countered example. My question is: Is there more countered examples?

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on $x_1,..,x_n,a_1,..a_n$. G.Sabbagh asked the following question: does an equation in $F$ have a solution if and only if it has a solution in any finite quotient? The answer is not and $[x^pa,y^{-1}z^pby]=t^q$ where $p$ and $q$ are two distance prime is a countered example. My question is: Are there more countered examples?