Ta có: \(M=\dfrac{13^{15}+1}{13^{16}+1}\)
\(13M=\dfrac{3^{16}+1}{3^{16}+1}\)
\(13M=1+\dfrac{12}{13^{16}+1}\)
\(N=\dfrac{13^{16}+1}{13^{17}+1}\)
\(13N=\dfrac{13^{17}+13}{13^{17}+1}\)
\(13N=1+\dfrac{12}{13^{17}+1}\)
Vì \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\) nên \(1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\)
\(\rightarrow M>N\)
Vậy \(M>N\)