query: Fermat's Combinatorial Identity: How to prove combinatorially?
positive_passages.docid: 36786
positive_passages.text: Prove $\sum\limits_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k}$ (a.k.a. Hockey-Stick Identity)
negative_passages.docid: 81729
negative_passages.text: Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion
negative_passages.docid: 116461
negative_passages.text: Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
negative_passages.docid: 60712
negative_passages.text: Induction Proof: Fibonacci Numbers Identity with Sum of Two Squares
negative_passages.docid: 35167
negative_passages.text: Prove congruence using fermat's thm
negative_passages.docid: 56828
negative_passages.text: A combinatorial proof that the alternating sum of binomial coefficients is zero
negative_passages.docid: 27585
negative_passages.text: Combinatorial proof of Stirling Number Identity (First Kind)
negative_passages.docid: 92440
negative_passages.text: Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
negative_passages.docid: 125174
negative_passages.text: Combinatorial intuition of identity
negative_passages.docid: 137175
negative_passages.text: Fermat's little theorem proof by Euler
negative_passages.docid: 20346
negative_passages.text: 'Algebraic' way to prove the boolean identity $a + \overline{a}*b = a + b$
negative_passages.docid: 146053
negative_passages.text: Proving identities (mod $pq$) using Fermat's little theorem?
negative_passages.docid: 108688
negative_passages.text: An identity involving products of sums
negative_passages.docid: 75910
negative_passages.text: Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
negative_passages.docid: 133181
negative_passages.text: Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
negative_passages.docid: 107021
negative_passages.text: Finding a combinatorial argument for an interesting identity: $\sum_k \binom nk \binom{m+k}n = \sum_i \binom ni \binom mi 2^i$
negative_passages.docid: 122006
negative_passages.text: Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"