Number theoretic proof for $n \choose k$ is a natural number without induction
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The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
37783
Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
124917
Fibonacci numbers and proof by induction
28942
About Math notation: the set of the first $n$ natural numbers
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Uncountable subset with uncountable complement, without the Axiom of Choice
149423
(combinatorics) prove that on average, n-permutations have Hn cycles without mathematical induction.
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
65742
Strong Induction: Every natural number $n\geq 8$ can be represented as $n=3k + 5\ell$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
46946
Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
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Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
140140
An identity which applies to all of the natural numbers
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${n\choose 2} - {k\choose 2} = {n-k\choose 2} +k(n-k)$ Marked box or unmarked box
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Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
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Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.
88880
Induction Proof $4^k < 5^k$