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Omni-MATH / Find all integers n≥3 for which there exist real numbers a₁,a₂,…a_(n+2) satisfying a_(n+1)=a₁, a_(n+2)=a₂ and a_(i)a_(i+1)+1=a_(i+2), for i=1,2,…,n. [i]

Problem

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problem

Find all integers n≥3n \geq 3 for which there exist real numbers a1,a2,…an+2a_1, a_2, \dots a_{n + 2} satisfying an+1=a1a_{n + 1} = a_1, an+2=a2a_{n + 2} = a_2 and aiai+1+1=ai+2,a_ia_{i + 1} + 1 = a_{i + 2}, for i=1,2,…,ni = 1, 2, \dots, n. [i]
Plain-text mathematical notation (without MathML)
Find all integers n≥3 for which there exist real numbers a₁,a₂,…a_(n+2) satisfying a_(n+1)=a₁, a_(n+2)=a₂ and
a_(i)a_(i+1)+1=a_(i+2),
for i=1,2,…,n.

[i]
Original LaTeX notation
Find all integers $n \geq 3$ for which there exist real numbers $a_1, a_2, \dots a_{n + 2}$ satisfying $a_{n + 1} = a_1$, $a_{n + 2} = a_2$ and
$$a_ia_{i + 1} + 1 = a_{i + 2},$$
for $i = 1, 2, \dots, n$.

[i]

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Source and history

task_id
32400288-8785-5bcb-a6fa-3df705d789ef
task_key
test--32400288-8785-5bcb-a6fa-3df705d789ef
task_revision_id
1
config / split
/ test

Official source

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