MHB 412.0.6 Find all integers n for which this statement is true, modulo n.

[karush]

for the equation $8\cdot8\cdot 8=4$. Find all integers $n$ for which this statement is true, modulo $n$.

ok so
$$8^3-(4)=508$$
508/4=127
508/127=4
then
2^2\cdot 127 = 508

ok I'm sure this is not the proper process

 

[Greg]

You were on the right track.

$$512\equiv4\pmod n\implies n=127,254,508$$

Further reading: https://en.wikipedia.org/wiki/Modular_arithmetic