3
6001 = 3 ⋅ (3
6000) = 3 ⋅ (3
6)
1000 = 3 ⋅ (729)
1000 = 3(728 + 1)
1000728 is divisible by 13, so the remainder is 3.
76000 = (74)1500 = (2401)1500 = (2392 + 9)15002392 is divisible by 13, so we have to find the remainder when 91500 is divided by 13.
91500 = (36)500 = (729)500 = (728 + 1)500
since 728 is divisible by 13, therefore the remainder is 1.
So the net remainder = 3 + 1 = 4