Let F be a finite field. Prove that there exists an integer n≥1,
such that n.1_F = 0_F .
Show further that the smallest positive integer with this
property is a prime number.
Prove that if the integers 1, 2, 3, . . . , 65 are arranged in
any order, then it is possible to look either left to right or
right to left through the list and find nine numbers that are in
increasing order
Prove that the language L={(M, N): M is a Turing machine and N
is a DFA with L(M) =L(N)} is undecidable. You need to derive a
reduction from Atm={(M, w)|Turing machine M accepts w} to L.
(In layman's terms please, no other theorems involved)