Idoneal number

In mathematics, Euler's idoneal numbers are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 is a prime, prime power, twice one of these, or a power of 2. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.


In mathematics, Euler's idoneal numbers are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 is a prime, prime power, twice one of these, or a power of 2. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.
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