Sums of Three Powers of Two

★ 7/10combinatorics number theory Modular Arithmetic Casework

Problem

Let

A = \left\{2^a + 2^b + 2^c \;:\; a, b, c \in \mathbb{N}\right\}

(the exponents need not be distinct). A subset $B \subseteq A$ consists of $n$ consecutive natural numbers. Find the maximum possible $n$ .

Answer

Solution

Difficulty	7/10
Topics	combinatorics, number theory, Modular Arithmetic, Casework

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