7+72+73+74+...+736=(7+72)+(73+74)+...+(735+736)
=7(1+7)+73(1+7)+...+735(1+7)
=(7+73+...+735).8 chia 8 dư 0
duyệt đi
71+72+........+736
=18x718
=4187349251769729
=(7^1+7^2)+............…+(7^35+7^36)
=7(1+7)+……………+7^35(1+7)
=7.8+…………………+7^35.8
suy ta: 7^1+7^2+………………+7^36 chia hết cho 8.
suy ra: 7^1+7^2+7^36 chia 8 dư 0
71 + 72 +.....+ 736
=718x18
->71 + 72 +.....+ 736 chia 8 dư 1
Đặt A = 71 + 72 + 73 + .... + 736
=> A = ( 71 + 72 ) + ( 73 + 74 ) + ..... + ( 735 + 736 )
=> A = 7 ( 1 + 7 ) + 72 ( 1 + 7 ) + .... + 735 ( 1 + 7 )
=> A = 7.8 + 72.8 + .... + 735.8
=> A = 8.( 7 + 72 + .... + 735 )
Vì 8 : 8 dư 0 => A : 8 dư 0
