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Omni-MATH / A deck of n>1 cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geomet…

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problem

A deck of n>1n > 1 cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards. For which nn does it follow that the numbers on the cards are all equal? [i]
Plain-text mathematical notation (without MathML)
A deck of n>1 cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards.
For which n does it follow that the numbers on the cards are all equal?

[i]
Original LaTeX notation
A deck of $n > 1$ cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards.
For which $n$ does it follow that the numbers on the cards are all equal?

[i]

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Source and history

task_id
54000be9-aa4a-5e15-88cd-bc7009b34bd3
task_key
test--54000be9-aa4a-5e15-88cd-bc7009b34bd3
task_revision_id
1
config / split
/ test

Official source

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