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Omni-MATH / Let's say we have a [i]nice[/i] representation of the positive integer n if we write it as a sum of powers of 2 in such a way that there are at most two equal powers in the sum (re…

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problem

Let's say we have a [i]nice[/i] representation of the positive integer n n if we write it as a sum of powers of 2 in such a way that there are at most two equal powers in the sum (representations differing only in the order of their summands are considered to be the same). a) Write down the 5 nice representations of 10. b) Find all positive integers with an even number of nice representations.
Plain-text mathematical notation (without MathML)
Let's say we have a [i]nice[/i] representation of the positive integer n if we write it as a sum of powers of 2 in such a way that there are at most two equal powers in the sum (representations differing only in the order of their summands are considered to be the same).

a) Write down the 5 nice representations of 10.

b) Find all positive integers with an even number of nice representations.
Original LaTeX notation
Let's say we have a [i]nice[/i] representation of the positive integer $ n$ if we write it as a sum of powers of 2 in such a way that there are at most two equal powers in the sum (representations differing only in the order of their summands are considered to be the same).

a) Write down the 5 nice representations of 10.

b) Find all positive integers with an even number of nice representations.

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Source and history

task_id
25623d2c-1871-544d-b4c6-fe256330f4ac
task_key
test--25623d2c-1871-544d-b4c6-fe256330f4ac
task_revision_id
1
config / split
/ test

Official source

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