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Omni-MATH / For positive integers a,b,a↑↑b is defined as follows: a↑↑1=a, and a↑↑b=a^(a↑↑(b−1)) if b>1. Find the smallest positive integer n for which there exists a positive integer a such th…

Problem

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problem

For positive integers a,b,a↑↑ba, b, a \uparrow \uparrow b is defined as follows: a↑↑1=aa \uparrow \uparrow 1=a, and a↑↑b=aa↑↑(b−1)a \uparrow \uparrow b=a^{a \uparrow \uparrow(b-1)} if b>1b>1. Find the smallest positive integer nn for which there exists a positive integer aa such that $a \uparrow \uparrow 6 \not \equiv a \uparrow \uparrow 7$ $\bmod n$.
Plain-text mathematical notation (without MathML)
For positive integers a,b,a↑↑b is defined as follows: a↑↑1=a, and a↑↑b=a^(a↑↑(b−1)) if b>1. Find the smallest positive integer n for which there exists a positive integer a such that $a \uparrow \uparrow 6 \not \equiv a \uparrow \uparrow 7$ $\bmod n$.
Original LaTeX notation
For positive integers $a, b, a \uparrow \uparrow b$ is defined as follows: $a \uparrow \uparrow 1=a$, and $a \uparrow \uparrow b=a^{a \uparrow \uparrow(b-1)}$ if $b>1$. Find the smallest positive integer $n$ for which there exists a positive integer $a$ such that $a \uparrow \uparrow 6 \not \equiv a \uparrow \uparrow 7$ $\bmod n$.

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Source and history

task_id
6971132c-3bef-58af-bdd0-6783c90915f3
task_key
test--6971132c-3bef-58af-bdd0-6783c90915f3
task_revision_id
1
config / split
/ test

Official source

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