Other
Four-Colors Theorem
In 1852 a South African mathematician, Francis Guthrie, was coloring a map of the counties of England a…
In 1852 a South African mathematician, Francis Guthrie, was coloring a map of the counties of England a…
Def : Every integer is greater then 1 is either a prime or can be written as a product of primes .
Def : Let a , b belong integer numbers , and n belongs to natural numbers . Then ax = b (mod n) Is calle…
Def : Let p be prime number , a belongs to integers , and p doesn't divide a . Then a^p-1 = 1 (mod p)
Def : If n belongs natural numbers , a belongs integers such that GCD(a , n) = 1 . Then a^Q(n) = 1 (mod n )…
Def : For n>=1 , let Q(n) denote the number of positive integers not exceeding n that are relatively prim…
Let a ,b belongs integers except {0} If a = q*b + r , then GCD(a,b)=GCD(b,r) . q: is called the quotient …
\begin{array}{l} Let\;\;\;\;a,b \in Z\;\;\;\;,\;\;\;\;b \in N\\ Then\;there\;exist\;unique\;\;\;\;\;q,r \…
Definition: Diophantine equation is any equation in one or more unknowns with integer coefficient and to be s…
Ex 1 : How many strings of length 4 be formed from the English alphabet with repetition allowed ? Ex 2 : …
We want to solve counting problems where element maybe used more than once . * Permutation with repetition …
If N objects are placed into K boxes , then there is at least one box containing at least \[\left\lceil …
If k is a positive integer and k+1 or more objects are placed into k boxes , then there is at least one box …
If I tell you to find the third derivative of (x³ eˣ) ''' It is expected to think of the deriva…
Inclusion Exclusion Rule A 1 ∪ A 2 ∪ . . . ∪ A n ≡ ∑ 1 ≤ i ≤ n A i - ∑ i ≠ j A i ∩ A j + ∑ d i f …