Last 4 digits of a^1000 Prediction?

[icedsake]

Homework Statement

for 2<= a <=10
what is the last 4 digits of a^1000?
What is the criterion for the prediction of the last 4 digits from a?

 

[transgalactic]

i am not sure
but it looks like a tailor series with calculating and error

 

[malawi_glenn]

use modulus when you divide a^1000 with 10000 ?

 

[icedsake]

would there be a formula?

 

[malawi_glenn]

you don't know how modulus work?

 

[PingPong]

Try using modulus and Euler's Theorem (if you're dealing with the prime a). Or you could try finding the order of a mod 10000 and using modulo arithmetic from there. That should reduce the problem to a much simpler one - at least, you won't have to multiply a out 1000 times.