An Easy Generalization of Euler's Theorem on the Series of Prime Reciprocals
نویسنده
چکیده
It is well-known that Euclid’s argument can be adapted to prove the infinitude of primes of the form 4k − 1. We describe a simple proof that the sum of the reciprocals of all such primes diverges. More generally, if q is a positive integer, and H is a proper subgroup of the units group (Z/qZ)×, we show that ∑ p prime p mod q 6∈H 1 p =∞.
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 122 شماره
صفحات -
تاریخ انتشار 2015