Woah

Une française

No, you can't !Can 7^1000 be broken down to 7^100 + 7^10?

Use the congruences (you learn it in last year of high school). As you want the digit in the units, study the congruence of 7^1000 to 10.

This is why you'll try the very first powers of 7 and see what is their congruence to 10.

So

Hence for all , 7^{4k} \equiv 1 [10][/tex]

-> as 1000 is 4*250,

So the digit unit will be 1.