Consider the set S of integers 1,2,...,n. Let 2$^k$ be the integer in S that is the highest power of 2. Prove that 2$^k$ is not a divisor of any other integer in S. I don't want a complete proof here. I just want to know how to approach this problem, so that I can write a formal proof.
2026-03-26 06:28:24.1774506504
Number Theory: Divisibility on a set of consecutive integers
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HINT: What is the smallest natural number $x$ that is divisible by $2^k$, where $x > 2^k$?