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New posts in natural-numbers
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
elementary-number-theory
factorial
gcd-and-lcm
natural-numbers
Prove that $\sqrt{n} \le \sum_{k=1}^n \frac{1}{\sqrt{k}} \le 2 \sqrt{n} - 1$ is true for $n \in \mathbb{N}^{\ge 1}$
inequality
induction
problem-solving
natural-numbers
Family set of subsets of $\Bbb N$
elementary-set-theory
natural-numbers
Finding all functions $f: \mathbb{Z^{+}}\to \mathbb{Z^{+}}$ such that $f(a)| (f(b)+a-b)$ for all $a,b\in \mathbb{Z^{+}}$
functions
divisibility
natural-numbers
Axiom schema and the definition of natural numbers
logic
axioms
natural-numbers
Examples of polynomial injections $f:\mathbb{N}\times \mathbb{N}\to \mathbb{N}$
number-theory
polynomials
soft-question
natural-numbers
Why don't we use Presburger's arithmetic instead of Peano's arithmetic?
number-theory
logic
natural-numbers
foundations
peano-axioms
What is the meaning of set-theoretic notation {}=0 and {{}}=1?
elementary-set-theory
math-history
natural-numbers
foundations
Sum of sum of $k$th power of first $n$ natural numbers.
number-theory
power-series
natural-numbers
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
elementary-number-theory
natural-numbers
Should $\mathbb{N}$ contain $0$? [closed]
soft-question
natural-numbers
Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
elementary-set-theory
order-theory
natural-numbers
Use an induction argument to prove that for any natural number $n$, the interval $(n,n+1)$ does not contain any natural number.
induction
natural-numbers
Show natural numbers ordered by divisibility is a distributive lattice.
divisibility
lattice-orders
natural-numbers
Is aleph-$0$ a natural number?
elementary-set-theory
cardinals
natural-numbers
Solve in $\mathbb N^{2}$ the following equation : $5^{2x}-3\cdot2^{2y}+5^{x}2^{y-1}-2^{y-1}-2\cdot5^{x}+1=0$
calculus
number-theory
natural-numbers
$\sqrt{17}$ is irrational: the Well-ordering Principle
number-theory
natural-numbers
Proof by induction that if $n \in \mathbb N$ then it can be written as sum of different Fibonacci numbers
induction
fibonacci-numbers
natural-numbers
Well Ordering implies Induction Proof doubt
proof-explanation
induction
natural-numbers
well-orders
How can we produce another geek clock with a different pair of numbers?
problem-solving
open-problem
natural-numbers
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