9 = 8+1

so look at (8+1)^1000, all the terms in the binomial expansion of this are

multiples of powers of 8 except for the last one, and so do not contribute to

the least significant digit base 8 of the result. So only 1^1000 contributes to

the ;east significant digit, but this is 1, so the least significant digit is 1.

11= 8+3

For the same reasons as above the least significant digit of 11^1000 is 3^1000

in base 8. But 3^1000 = 9^500, so in base 8 3^1000 = 9^500 which has least

significant digit 1 for the same reason as in the first part.

10=8+2

So using the same sort of argument as in the first part we know that the least

lsignificant digit base 8 is the least significant digit base 8 of 2^1000 base 8.

2^1000 = 2.2^999 = 2.8^333

so the least significant digit of 2^1000 in base 8 is 0.

RonL

RonL