Show that $5\mathbb{N}+3\mathbb{N}$={$0,3,5,6,8,9,10,11,12,...$}.
134454
Proof that every number ≥ $8$ can be represented by a sum of fives and threes.
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
15733
Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
31766
Prove that $a_{n}=0$ for all $n$, if $\sum a_{kn}=0$ for all $k\geq 1$
22592
$1\cdot 3 + 2\cdot 4 + 3\cdot 5 + \cdots + n(n+2) = n(n+1)(2n+7)/6$ by mathematical induction
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
142263
Assuming $ab^2 = b^3a$ and $a^2=1$ prove that the order of $b$ is $5$.
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
127400
Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5