ผมเจอการพิสูจน์ว่าจำนวนเฉพาะที่อยู่ในรูป 4k+1 มีจำนวนอนันต์ใครเข้าใจช่วยอธิบายหน่อยครับ
4. Suppose that there are only finitely many primes of the form $4k+1$,
say $q_1,...,q_r$, and consider $N=(q_1...q_r)^2+1. N > qi$, for
$1 < i < r,$ hence $N$ cannot be prime. Any number of the form $a^2+1$
has, except possibly for the factor $2$, only prime factors of the form
$4m+1$. Since division into N by each prime factor of the form $4k+1$
leaves a remainder $1, N$ cannot be composite, a contradiction. Hence,
the number of primes of the form $4k+1$ must be infinite.
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