number
16 theorems carry this thread across the degree.
The binomial theorem
An expansion of (x+y)^n in terms of binomial coefficients.
The inclusion–exclusion principle
The size of a union from the sizes of intersections.
The handshaking lemma
In any graph the sum of degrees is twice the number of edges.
Fermat's little theorem
a^p ≡ a (mod p) for prime p.
The Chinese remainder theorem
Congruences with coprime moduli have a unique joint solution.
Euler's theorem on circuits
A connected graph has an Eulerian circuit iff every vertex has even degree.
The Euclidean algorithm and Bézout's identity
The gcd is an integer combination of its arguments.
The fundamental theorem of arithmetic
Every integer factors uniquely into primes.
Euler's theorem
a^φ(n) ≡ 1 (mod n) for a coprime to n.
Wilson's theorem
(p−1)! ≡ −1 (mod p) exactly when p is prime.
The law of quadratic reciprocity
A reciprocal relationship between two primes being squares mod each other.
Ramsey's theorem
Complete disorder is impossible in large enough structures.
Hall's marriage theorem
A matching exists iff every set of vertices has enough neighbours.
The max-flow min-cut theorem
Maximum flow equals minimum cut capacity.
Kuratowski's theorem
A graph is planar unless it contains K5 or K3,3.
Turán's theorem
The maximum edges in a graph with no large clique.