Explaining your logic, what is the final digit of the number 3^1001?
*I'm guessing that they don't want you to use a calculator?
Thank you.
Hello,
You can see it by iterations...
So you can see that there are only 4 possible values : 1;3;7;9. When you multiply by 3 a number which finishes by 3, the result will finish by 9. When you multiply by 3 a number which finishes by 9, the result will finish by 7, etc... You can prove it by writing that these numbers are for example.. When multiplying by 3, it yields , which obviously has its final digit number equal to 9
You can notice that the same value comes back every time you add 4 to the power.
For example : will have the same final digit number.
So continuing this way, if I add 25 times 4 to the power, it will be , which will have the same final digit number as
What is it going to be for ?
(I hope this is clear enough :/)