Simplifying help: If ${n \choose 3} + {n+3-1 \choose 3} = (n)_3$, compute $n$.
56566
If ${n \choose 3} + {n+3-1 \choose 3} = (n)_3$, compute $n$.
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
85195
Recurrence relation: $a_n = 3a_{n-1} + 2n, a_0 = 1$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
75457
How do i simplify the following: $\sum_{i=1}^n (3i^2+4) - \sum_{j=2}^{n+1} (3j^2+1)$
424
Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
115264
Find when three numbers have the same remainder when divided by the same number
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
106008
Combinatorial Identity $(n-r) \binom{n+r-1}{r} \binom{n}{r} = n \binom{n+r-1}{2r} \binom{2r}{r}$
48655
Find all n such that : $3 \mid (n2^{n}+1)$
47052
How can I simplify this expression involving binomial coefficients?
143409
Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
133150
Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$