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Omni-MATH / Let p>3 be a prime and let a₁,a₂,...,a_((p−1)/(2)) be a permutation of 1,2,...,(p−1)/(2). For which p is it always possible to determine the sequence a₁,a₂,...,a_((p−1)/(2)) if it …

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problem

Let p>3p>3 be a prime and let a1,a2,...,ap−12a_1,a_2,...,a_{\frac{p-1}{2}} be a permutation of 1,2,...,p−121,2,...,\frac{p-1}{2}. For which pp is it always possible to determine the sequence a1,a2,...,ap−12a_1,a_2,...,a_{\frac{p-1}{2}} if it for all i,j∈{1,2,...,p−12}i,j\in\{1,2,...,\frac{p-1}{2}\} with $i\not=j$ the residue of aiaja_ia_j modulo pp is known?
Plain-text mathematical notation (without MathML)
Let p>3 be a prime and let a₁,a₂,...,a_((p−1)/(2)) be a permutation of 1,2,...,(p−1)/(2). For which p is it always possible to determine the sequence a₁,a₂,...,a_((p−1)/(2)) if it for all i,j∈{1,2,...,(p−1)/(2)} with $i\not=j$ the residue of a_(i)a_(j) modulo p is known?
Original LaTeX notation
Let $p>3$ be a prime and let $a_1,a_2,...,a_{\frac{p-1}{2}}$ be a permutation of $1,2,...,\frac{p-1}{2}$. For which $p$ is it always possible to determine the sequence $a_1,a_2,...,a_{\frac{p-1}{2}}$ if it for all $i,j\in\{1,2,...,\frac{p-1}{2}\}$ with $i\not=j$ the residue of $a_ia_j$ modulo $p$ is known?

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Source and history

task_id
8dd9be2f-976f-588f-962a-5167bd4ea648
task_key
test--8dd9be2f-976f-588f-962a-5167bd4ea648
task_revision_id
1
config / split
/ test

Official source

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