Ta có :
51 . $5^{n}$ + 8 . $64^{n}$
= ( 59 - 8 ). $5^{n}$ + 8 . $64^{n}$
= 59 . $5^{n}$ - 8 . $5^{n}$ + 8 . $64^{n}$
= 59 . $5^{n}$ + 8 . ( $64^{n}$ - $5^{n}$ ) ⋮ 59
Vì $64^{n}$ - $5^{n}$ ⋮ ( 64 - 5 ) = 59
Vậy 51 . $5^{n}$ + 8 . $64^{n}$ ⋮ 59
#BTS
Xin ctlhn!