# Tagged Questions

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### For $n\ge4$, prove that $1!+2!+\cdots+n!$ cannot be the square of a positive integer

I'm trying to prove this by induction but seem to be getting nowhere.
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### Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$

How would you go about proving that $$\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$$ for any two integers $a$ and $b$? Intuitively it is true because when you divide $a$ and $b$ by ...
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### Proof Synopsis of Fermat's Last Theorem

I'm taking a introduction to higher math course now (mostly number theory) and our professor wants us to include two sentence proof synopses with our longer proofs. This got me thinking, What is a ...
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### My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

What do you think about my first proof that uses the well-ordering principle? Please mark/grade. Theorem The sum of the cubes of three consecutive natural numbers is a multiple of 9. Proof ...
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### My first proof employing strong induction / complete induction (very simple number theory). Please mark/grade.

What do you think about my first proof employing strong induction? What mark/grade would you give me? Theorem Every natural number greater than 1 is a product of one or more primes. Proof First, ...
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What do you think about my first induction proof? Please mark/grade. Theorem The sum of the cubes of three consecutive natural numbers is a multiple of 9. Proof First, introducing a predicate ...
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### Prove or disprove: If $A$ and $B$ are denumerable, then $A - B$ is denumerable
Prove or disprove: If $A$ and $B$ are denumerable, then $A - B$ is denumerable Can someone give me a hint as to how to prove/disprove this? My instinct tells me that the claim is true. But I'm ...