Problem
NT-B2-M04-P003 Inverse Element
#3
★★☆☆☆ Level 2 of 5
Find the inverse of \(7\) modulo \(13\).
Compute directly or use \(7^{11}\).
Directly, \(7\cdot2=14\equiv1\pmod{13}\). Thus the inverse is \(2\). This agrees with Fermat: \(7^{12}\equiv1\), so \(7^{11}\) is also an inverse.
This connects Fermat with invertible residues.