ON ERD˝oS'S DISTINCT SUBSET SUMS CONJECTURE VIA THE CIRCLE METHOD

We investigate Paul Erdős's conjecture on distinct subset sums. For any set \( A = \{a_1 < \cdots < a_n\} \subset \mathbb{N} \) with distinct subset sums, we prove the lower bound \(\max(A) \geq c \cdot 2^n\) for some absolute constant \(c > 0\). Our approach combines the circle method with techniques from additive combinatorics, establishing new connections between the distribution of subset sums and exponential sums over major arcs.