First:
Observe that:
mod 10
mod 10
so we observe that: mod 10
Thus mod 10
So you answer is incorrect. And the steps you take don't allways make sense.
2.
mod 20
mod 20
mod 20
Observe that mod 20
Thus:
mod 20
mod 20
mod 20
mod 20
Just want some confirmation on what i've done -number theory's my weakest area by far.
1. Calculate 7^23 (mod 10)
MY ANSWER: 7=17 (mod 10)
7^2 = 289 = 9(mod 10)
so 7^22 = (7^2)^11 = 9 (mod 10)
so 7^23 = 7 x 7^22 = 17 x 9^11 = 9(mod 10)
(note: these are meant to be equivalent rather than equals signs)
2. Solve 8x = 12 (mod 20)
MY ANSWER:
gcd(8,20) = 4
4 divides 12 so there are 3 solutions.
A solution is x = 14 (by observation).
Solutions differ by 20/4 = 5.
So 9 and 4 are other solutions as general solutuons given by x= u - (n/d)t
First:
Observe that:
mod 10
mod 10
so we observe that: mod 10
Thus mod 10
So you answer is incorrect. And the steps you take don't allways make sense.
2.
mod 20
mod 20
mod 20
Observe that mod 20
Thus:
mod 20
mod 20
mod 20
mod 20