MathDB

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)}

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

26