Does the statement the are an infinite number of primes p, such that for any j, $1
$pj\equiv b$ mod a
imply dirichlets theorem? that there are an infinite number of primes p such that $p\equiv b$ mod a,
for constants b and a
Does the statement the are an infinite number of primes p, such that for any j, $1
$pj\equiv b$ mod a
imply dirichlets theorem? that there are an infinite number of primes p such that $p\equiv b$ mod a,
for constants b and a
Dirichlet's theorem: For positive integers $a,b$ with $(a,b)=1$ there exist infinitely many primes $p$ with $p\equiv b\mod a$. Your statement (or what your statement should be): For positive integers $a,b$ with $(a,b)=1$ and $1
Your statement implies Dirichlet's theorem: Let $a,b$ be positive integers with $(a,b)=1$ and $a>2$. Let $1
The case $a=2$ only says that there are infinitely many odd primes. :)