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1.733 368 733 × 10 1 000: ... [1] Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain ...
A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS ). 0! = 1 is sometimes included.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. [1] [2] [3] The name ... [10] Cycles 2 3 ...
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). [1]The first 10 factorial primes (for n ...
f has degree at most p − 2 (since the leading terms cancel), and modulo p also has the p − 1 roots 1, 2, ..., p − 1. But Lagrange's theorem says it cannot have more than p − 2 roots. Therefore, f must be identically zero (mod p), so its constant term is (p − 1)! + 1 ≡ 0 (mod p). This is Wilson's theorem.
In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. [1] [2] [3]
In this case the problem reduces to n − 2 people and n − 2 hats, because P 1 received h i ' s hat and P i received h 1 's hat, effectively putting both out of further consideration. For each of the n − 1 hats that P 1 may receive, the number of ways that P 2 , ..., P n may all receive hats is the sum of the counts for the two cases.