Problem
NT-B1-M07-P005 When Euler Cannot Be Used
#5
★☆☆☆☆ Level 1 of 5
Explain why Euler's theorem cannot be applied to \(2^{10}\) modulo \(8\), and find the remainder.
Check \(\gcd(2,8)\).
\(\gcd(2,8)=2\ne1\), so Euler's theorem cannot be used. But \(2^3=8\equiv0\pmod8\), so every \(2^n\) with \(n\ge3\) is divisible by \(8\). Hence \(2^{10}\equiv0\pmod8\).
A very important anti-mistake.