Question

What are the last 2 digits of the number 43^34?

Answer 1

what are the first few powers of 43,

Answer 2

Mathematica:

Table[43^n, {n, 1, 5, 1}]
{43, 1849, 79507, 3418801, 147008443}

Answer 3

Looks like it returns to 43 every 5 powers.

Answer 4

\[43^{34}= 43*43*43^{32}=1849*43^{32}=1849*43*43^{31}=147008443*43^{31}\]

Answer 5

for every power of 5 we have a 43 and since its a 3 at one's place we can have 9 at the one place of the 34th power

Answer 6

use modulo 100 on the powers of 43
43^0 01
43^1 43
43^2 49 mod 100
43^3 07
43^4 01 it starts repeating

43^32 = 43^0 mod 100
43^34= 43^2
=49 as the last 2 digits