71+72+73+74+75+76
=7.(7+1) + \(7^3.\left(1+7\right)\)+ \(7^5.\left(1+7\right)\)
=\(7.8+7^3.8+7^5.8\)
=\(8.\left(7+7^3+7^5\right)\)
vì 8 \(⋮\)8 nên \(8.\left(7+7^3+7^5\right)⋮8\)
nên \(7^1+7^2+7^3+7^4+7^5+7^6\)chia hết cho 8
71+72+73+74+75+76
=(71+72) + (73+74) + (75+76)
=7(7+1) + 73(1+7) + 75(1+7)
=7x8 + 73x8 + 75x8
(vì mỗi số hạng chia hết cho 8)
71\(+\)72\(+\)73\(+\)..\(+\)76 \(⋮\) cho 8
=(71\(+\)72)+(73\(+\)74)+(75\(+\)76)
=7(1\(+\)7)\(+\)73(1\(+\)7)\(+\)75(1\(+\)7)
\(\Rightarrow\)7\(\times\)8\(+\)73\(\times\)8\(+\)75\(\times\)8
vì ta thấy 8\(⋮\)nên
\(\Rightarrow\)(7\(\times\)8\(+\)73\(\times\)8\(+\)75\(\times\)8)\(⋮\)8
hay( 71\(+\)72\(+\)....\(+\)76)\(⋮\)8 (đpcm)
