Question

A= 145^n+23-145^n+22

chứng tỏ A chia hết cho 18

Answer 1

\(A=145^{n+23}-145^{n+22}\\=145^{n+22}\cdot145-145^{n+22}\\=145^{n+22}\cdot(145-1)\\=145^{n+22}\cdot144\\=145^{n+22}\cdot18\cdot8\)

Vì \(145^{n+22}\cdot18\cdot8\vdots18\)

nên \(A\vdots18\)