C = 2 + 22 + 23 + .. + 299 + 2100
= 2(1 +2 + 22+ 23+ 24) + 26(1 + 2 + 22+ 23+ 24)+....+ (1 + 2 + 22+ 23+ 24).296
= 2 . 31 + 26 . 31 + .... + 296 . 31
= 31(2 + 26 +....+296). Vậy C chia hết cho 31
C = 2 + 22 + 23 + .. + 299 + 2100
= ( 2 + 22 + 23 + 24 + 25 +26 ) + .......+ ( 295+296+297+298+299 + 2100)
= 2(1 +2 + 22+ 23+ 24) + 26(1 + 2 + 22+ 23+ 24)+....+ (1 + 2 + 22+ 23+ 24).296
= 2 . 31 + 26 . 31 + .... + 296 . 31
= 31(2 + 26 +....+296). Vậy C chia hết cho 31
C = 2 + 22 + 23 + .. + 299 + 2101
= ( 2 + 22 + 23 + 24 + 25 +26 ) + .......+ ( 295+296+297+298+299 + 2101)
= 2(1 +2 + 22+ 23+ 24) + 26(1 + 2 + 22+ 23+ 24)+....+ (1 + 2 + 22+ 23+ 24).296
= 2 . 31 + 26 . 31 + .... + 296 . 31
= 31(2 + 26 +....+296). Vậy C chia hết cho 31
C = 2 + 22 + 23 + .. + 299 + 2100
= 2(1 +2 + 22+ 23+ 24) + 26(1 + 2 + 22+ 23+ 24)+....+ (1 + 2 + 22+ 23+ 24).296
= 2 . 31 + 26 . 31 + .... + 296 . 31
= 31(2 + 26 +....+296). Vậy C chia hết cho 31