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Dirichlet's theorem states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer.
Dirichlet's theorem states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer.
- There are a finite number of primes of the form a + nd, where n is a positive integer.
- There are only a few primes of the form a + nd, where n is a positive integer.
- There are no primes of the form a + nd, where n is a positive integer.
- There are infinitely many primes of the form a + nd, where n is a positive integer. (correct)
What does a and d represent in Dirichlet's theorem?
What does a and d represent in Dirichlet's theorem?
- a represents a negative integer and d represents a positive integer.
- a represents a negative integer and d represents a negative integer.
- a represents a positive integer and d represents a negative integer.
- a represents a positive integer and d represents a positive integer. (correct)
What is the arithmetic progression formed by the numbers of the form a + nd?
What is the arithmetic progression formed by the numbers of the form a + nd?
- a, a - d, a - 2d, a - 3d, ...
- a, a + d, a + 2d, a + 3d, ... (correct)
- a, a * d, a * 2d, a * 3d, ...
- a, a / d, a / 2d, a / 3d, ...
What does Euclid's theorem state?
What does Euclid's theorem state?
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What do stronger forms of Dirichlet's theorem state?
What do stronger forms of Dirichlet's theorem state?
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