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Omni-MATH / For which positive integers m does there exist an infinite arithmetic sequence of integers a₁,a₂,... and an infinite geometric sequence of integers g₁,g₂,... satisfying the followi…

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problem

For which positive integers mm does there exist an infinite arithmetic sequence of integers a1,a2,...a_1, a_2, . . . and an infinite geometric sequence of integers g1,g2,...g_1, g_2, . . . satisfying the following properties? [list] [*] an−gna_n - g_n is divisible by mm for all integers n≥1n \ge 1; [*] a2−a1a_2 - a_1 is not divisible by mm. [/list] [i]Holden Mui[/i]
Plain-text mathematical notation (without MathML)
For which positive integers m does there exist an infinite arithmetic sequence of integers a₁,a₂,... and an infinite geometric sequence of integers g₁,g₂,... satisfying the following properties?
[list]
[*] a_(n)−g_(n) is divisible by m for all integers n≥1;
[*] a₂−a₁ is not divisible by m.
[/list]
[i]Holden Mui[/i]
Original LaTeX notation
For which positive integers $m$ does there exist an infinite arithmetic sequence of integers $a_1, a_2, . . .$ and an infinite geometric sequence of integers $g_1, g_2, . . .$ satisfying the following properties?
[list]
[*] $a_n - g_n$ is divisible by $m$ for all integers $n \ge 1$;
[*] $a_2 - a_1$ is not divisible by $m$.
[/list]
[i]Holden Mui[/i]

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Source and history

task_id
e1b3e815-ac9a-54c4-be13-3e34c5115de8
task_key
test--e1b3e815-ac9a-54c4-be13-3e34c5115de8
task_revision_id
1
config / split
/ test

Official source

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