a[i] denote number of friends i-th student has. c[j] denote frequency having at least j friends. Show that: ∑a[i]=∑c[j].
112237
prove this :$\sum_1^{100} A_i = \sum_0^{99} C_i $
59831
How to relate combinatorial proof to bipartite graphs?
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
39753
Proving that in a simple graph with $n$ vertices, two vertices have the same degree
98518
Cardinality of equivalence relations on N
32795
Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.
127237
Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$.
906
Pigeonhole Principle Question - Group of 6 people, do 3 either know each other or not?
61483
Prove the following identity combinatorially
114522
Prove that identity is unique in a group
42062
Interpretation of a combinatorial expression
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
145397
How to prove that for every $i$, $a_i = i$
26343
Number of certain (0,1)-matrices, Stanley's Enumerative Combinatorics
122959
How is number of conjugacy class related to the order of a group?