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math.NT2026
An update on the Linnik--Goldbach problem
Daniel R. Johnston, Tim Trudgian
We consider the Linnik--Goldbach problem of writing all large even integers as the sum of two primes and a fixed number of powers of 2. We show that, under the generalised Riemann…
math.NT2026
The infinitude of square-free palindromes
Daniel R. Johnston, Bryce Kerr
We settle an open problem regarding palindromes; that is, positive integers which are the same when written forwards and backwards. In particular, we prove that for any fixed base…