what is the remainder ?

Question

6^83^83^83 divided by 83 ?

I meant 6 raised to 83 raised to 83 and so on.So i dont think we can write as 83 raised to 3

Answer 1

an enormous number..!!!
calculator gave up

Answer 2

83 is a prime number. Since it doesnt divede 6, it doesnt divide any power of 6. By Fermat's Little Theorem, we have (6^83^83)^83 = (6^83)^83 (mod 83).(hre, = means congrtuent to modulus 83)Again, (6^83)^83 = 6^83 (mod 83), and still 6^83 = 6 mod (83). Since congruence is a transitive relation, it follows 6^83^83^83 = 6 (mod 83), so that the remainder of the division of 6^83^83^83 by 83 equal the remainder of the division of 6 by 83. Therefore, the desired remainder is 6.

Remark: I'm assuming you mean ((6^83^)^83)^83, which is the same the 6^(83^3)

Answer 3

It's what's left over after the division operation.