47? Easy!

Number Theory Level pending

$\large ^4 7 \equiv 7^A \pmod{660}$

Find the minimum integer value of $A$ satisfying the equation above.

Notation : $_{ }^{ y }{ x }$ is the tetration function

1 solution

Otto Bretscher
Mar 12, 2016

Since $\lambda(660)=20$ and $\lambda(20)=4$ , the Carmichael Lambda , we have $7^{7^{7^7}}=7^{7^{3}}\equiv 7^{\boxed{3}}\pmod{660}$