00:01
Hello, the question deals with little format's theorem which states that a raised to the part p minus 1 is equal to 1 mod p where p is prime.
00:15
So for the first part 512 raised to the par 372 mod 13 this can be expressed as 512 r.
00:31
To the power 13 minus 1 is equal to 1 mod 13.
00:39
512 to the part 12 is equals to 1 mod 13.
00:48
512 raised to the power 12 whole raise to the power 31 is equals to 1 raised to the power 31 mod 13.
01:00
So 512 raised to the par 372 is equal to 1 mod 13.
01:12
So the required value of the expression is 1.
01:18
For the next expression we again use the little format theorem 3, 4, 4, 4, 4 raise to the par 16 is 1 mod 17 3 4 4 4 raise to the power 16 4 raise to the power 202 into 3 4 4 4 is equal to 3 4 4 4 4 mod 17 now this can be simplified as 3 ,44 raised to the power 3232 times 344 is equal to 3144 mod 17.
02:28
Next 3, 444 raise to the power 3, 444, 3 ,000...