Which number comes next?
This paper is not highly recommended, since it was written in a state of great ignorance.
Kind correspondents have written to me to answer the question raised in the coda of this paper.
Here's the answer courtesy of James Swenson:
By Dirichlet's theorem, there are infinitely many primes of the form p=4n+1. Fermat and Euler showed that all such primes are expressible as sums of two squares. Moreover these expressions are unique up to permutation. This resolves your conjecture: there are infinitely many integers that can only be expressed as the sum of two squares in one way.
Thank you for an interesting puzzle!
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