List questions from integers

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Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n

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List Question

Factor $x^8 - x$ into irreducibles in $\mathbb{Z}[x].$

Getting smallest positive number

Properties of $\mathbb{Z}_n$ where n is square free

Proof of sum of consecutive integers

Proof that the sqrt of a Natural Number is irrational outside of square numbers.

Show $\sum_{k=1}^n \frac{1}{k^2} \le 2$ and $\ln(n!) \ge 1 -n+n\ln(n)$ for all positive integers n

What is the name given to the triangle patterns when marking on a table of integers that gives an integer when one is divided by the other?

Proving an expression is an integer (number theory)

Is it correct to say that the natural numbers are a proper subset of the integers?

Find all possible values of c

On the least prime in an arithmetic progression $a + nb$ where $a,b$ are distinct primes.

etymology of smoothness

Greatest Common Divisors of powers - 1?

Z denotes the set of integers, but what is $Z[i]$

Diophantine equation of 2nd order

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