Vantieghems theorem
In number theory, Vantieghem's theorem is a primality criterion. It states that a natural number n≥3 is prime if and only if ∏ 1 ≤ k ≤ n − 1 ( 2 k − 1 ) ≡ n mod ( 2 n − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(2^{k}-1\right)\equiv n\mod \left(2^{n}-1\right).} Similarly, n is prime, if and only if the following congruence for polynomials in X holds: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n − ( X n − 1 ) / ( X − 1 ) mod ( X n − 1 ) {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n-\left(X^{n}-1\right)/\left(X-1\right)\mod \left...
Nº Q2226807 ★★
Uncommon · Knowledge
Vantieghems theorem
In number theory, Vantieghem's theorem is a primality criterion. It states that a natural number n≥3 is prime if and only if ∏ 1 ≤ k ≤ n − 1 ( 2 k − 1 ) ≡ n mod ( 2 n − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(2^{k}-1\right)\equiv n\mod \left(2^{n}-1\right).} Similarly, n is prime, if and only if the following congruence for polynomials in X holds: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n − ( X n − 1 ) / ( X − 1 ) mod ( X n − 1 ) {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n-\left(X^{n}-1\right)/\left(X-1\right)\mod \left...
Last price
—
Floor price
—
7-day median
—
30-day sales
0
30-day range
—
In circulation
0
Price history
median
low – high
sales
No sales in this period
Show table
| Date | median | Low | High | sales |
|---|
Sales history
- Last sale
- —
- 30-day average
- —
- 30-day low
- —
- 30-day high
- —
- Sales 7d
- 0
- Sales 30d
- 0
No sales yet.
Anonymous sales: no buyer or seller shown. Figures count player-to-player sales only.
From Wikipedia
In number theory, Vantieghem's theorem is a primality criterion. It states that a natural number n≥3 is prime if and only if ∏ 1 ≤ k ≤ n − 1 ( 2 k − 1 ) ≡ n mod ( 2 n − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(2^{k}-1\right)\equiv n\mod \left(2^{n}-1\right).} Similarly, n is prime, if and only if the following congruence for polynomials in X holds: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n − ( X n − 1 ) / ( X − 1 ) mod ( X n − 1 ) {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n-\left(X^{n}-1\right)/\left(X-1\right)\mod \left(X^{n}-1\right)} or: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n mod ( X n − 1 ) / ( X − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n\mod \left(X^{n}-1\right)/\left(X-1\right).}
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
Bertrand's postulate
Theorem
Nº Q632546 ★★
Fermat's little theorem
Mathematical theorem that, for any prime 𝑝, the 𝑝th power of any integer 𝑛 is congruent to 𝑛 modulo 𝑝
Nº Q188295 ★★★
Wilson's theorem
Necessary and sufficient condition for a number to be prime
Nº Q276082 ★★
Well-ordering principle
Statement that all sets of positive numbers contains a least element
Nº Q2488476 ★★★
Wolstenholme's theorem
Theorem
Nº Q1724049 ★★★
Euler's theorem
Generalization of Fermat's little theorem, that given coprime positive integers 𝑛 and 𝑎, then the φ(𝑛)-th power of 𝑎 is congruent to 1 modulo 𝑛, where φ is Euler’s totient function
Nº Q193910 ★★