MathDB

2016 Guts #26

Source:

December 24, 2016

Problem Statement

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

mod

n

.

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