# Tagged Questions

For questions about approaches and techniques for discovering a proof, as opposed to writing it down clearly (which involves (proof-writing)). Should not be used unless the focus is on the technique of the proof instead of the solution.

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### reflexive, symmetric, and transitive relations proof

Let $A = \{1, 2, 3, ... , n\}$ where $n$ is a positive integer. Let $F$ be the set of all functions from $A$ to $A$. Let $R$ be the relation on $F$ defined by: for all $g, f \in F, fRg$ if and only ...
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### Proof reflexive, symmetric and transitive relations

Let $A = \{1, 2, 3, ... , n\}$ where $n$ is a positive integer. Let $F$ be the set of all functions from $A$ to $A$. Let $R$ be the relation on $F$ defined by: for all $g, f \in F, fRg$ if ...
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### Proving that $b^6-2a^3b^3-2b^3+a^6-2a^3+1$ is never a nontrivial integer square?

I'm trying to prove that if $a,b$ are integers, and $b^6-2a^3b^3-2b^3+a^6-2a^3+1$ is a square [integer], then $ab=0$. What general tools are available to attack such a problem?
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### Proof of onto and one-to-one functions, composition

I want to prove this: Let $f: A \to B$ and $g: B \to C$ be functions. if $g \circ f$ is onto, and $g$ is one-to-one, then f is onto. Here is what I have done, can someone please verify my work: ...
So I was given multiple questions of computing the GCD of $\gcd(10;45)$ and $\gcd(1701;3768)$, etc. The questions generally worked with numbers and I was able to solve it quite simply since I knew ...