Problem
NT-B1-M12-P017 Set 4. Power and Divisibility
#17
★★★☆☆ Level 3 of 5
Prove that \(5\mid2^{4n}-1\) for every positive integer \(n\).
Find \(2^4\pmod5\).
Since \(2^4=16\equiv1\pmod5\), \(2^{4n}=(2^4)^n\equiv1^n\equiv1\pmod5\). Hence \(5\mid2^{4n}-1\).
Short order/cycle task.