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Omni-MATH / Consider the assertion that for each positive integer n≥2 , the remainder upon dividing 2^(2^(n)) by 2^(n)−1 is a power of 4. Either prove the assertion or find (with proof) a coun…

Problem

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problem

Consider the assertion that for each positive integer

n \ge 2

, the remainder upon dividing

2^{2^n}

2^n-1

is a power of 4. Either prove the assertion or find (with proof) a counter-example.

Plain-text mathematical notation (without MathML)

Consider the assertion that for each positive integer n≥2 , the remainder upon dividing 2^(2^(n)) by 2^(n)−1 is a power of 4. Either prove the assertion or find (with proof) a counter-example.

Original LaTeX notation

Consider the assertion that for each positive integer $n \ge 2$ , the remainder upon dividing $2^{2^n}$ by $2^n-1$ is a power of 4. Either prove the assertion or find (with proof) a counter-example.

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task_id: 12e4d184-cf57-53d2-bbce-5c4149c86352
task_key: test--12e4d184-cf57-53d2-bbce-5c4149c86352
task_revision_id: 2
config / split: / test

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