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MATH / Let the term S_(n) be the sum of the first n powers of 2. For instance, S₃=2⁰+2¹+2²=7. Find the largest possible value of the greatest common divisor of two consecutive terms, …

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problem

Let the term SnS_n be the sum of the first nn powers of 22. For instance, S3=20+21+22=7S_3 = 2^0 + 2^1 + 2^2 = 7. Find the largest possible value of the greatest common divisor of two consecutive terms, SnS_n and Sn+1S_{n+1}, for any nn.
Plain-text mathematical notation (without MathML)
Let the term S_(n) be the sum of the first n powers of 2. For instance, S₃=2⁰+2¹+2²=7.  Find the largest possible value of the greatest common divisor of two consecutive terms, S_(n) and S_(n+1), for any n.
Original LaTeX notation
Let the term $S_n$ be the sum of the first $n$ powers of $2$. For instance, $S_3 = 2^0 + 2^1 + 2^2 = 7$.  Find the largest possible value of the greatest common divisor of two consecutive terms, $S_n$ and $S_{n+1}$, for any $n$.

level

Level 4

type

Number Theory

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Source and history

task_id
4cf6ce69-58ad-5803-8efe-24ef4e35c3de
task_key
number~5ftheory--test--4cf6ce69-58ad-5803-8efe-24ef4e35c3de
task_revision_id
1
config / split
number_theory / test

Official source

initial import