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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…

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problem

Consider the assertion that for each positive integer n≥2n \ge 2 , the remainder upon dividing 22n2^{2^n} by 2n−12^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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Source and history

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

Official source

initial import