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For any , if is a sufficiently large finite Sidon set then there are at least many such that .
Source: erdosproblems.com/152
An accepted solution exists. The statement is true.
PROVED (LEAN): a Lean proof by the DeepMind prover agent, posted 2026-04-03 and accepted by the site's curator on 2026-05-16, gives such sums; the acceptance and the Lean qualifications are on the claim page below.