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Omni-MATH / If a and b are positive integers that can each be written as a sum of two squares, then ab is also a sum of two squares. Find the smallest positive integer c such that c=ab, where …

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problem

If aa and bb are positive integers that can each be written as a sum of two squares, then aba b is also a sum of two squares. Find the smallest positive integer cc such that c=abc=a b, where a=x3+y3a=x^{3}+y^{3} and b=x3+y3b=x^{3}+y^{3} each have solutions in integers (x,y)(x, y), but c=x3+y3c=x^{3}+y^{3} does not.
Plain-text mathematical notation (without MathML)
If a and b are positive integers that can each be written as a sum of two squares, then ab is also a sum of two squares. Find the smallest positive integer c such that c=ab, where a=x³+y³ and b=x³+y³ each have solutions in integers (x,y), but c=x³+y³ does not.
Original LaTeX notation
If $a$ and $b$ are positive integers that can each be written as a sum of two squares, then $a b$ is also a sum of two squares. Find the smallest positive integer $c$ such that $c=a b$, where $a=x^{3}+y^{3}$ and $b=x^{3}+y^{3}$ each have solutions in integers $(x, y)$, but $c=x^{3}+y^{3}$ does not.

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Source and history

task_id
26094c0b-4490-5b37-a4bc-9f2984e028e0
task_key
test--26094c0b-4490-5b37-a4bc-9f2984e028e0
task_revision_id
1
config / split
/ test

Official source

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