I NEED THE COUNTEREXAMPLE Q: for A set of natural numbers, define binary A = {binary representations of numbers in A} contained (0 + 1)*, urnary A = {0^n | n in A} contained 0*. For example, if A = {2, 3, 5}, then binary A = {10, 11, 101}, unary A ={00, 000, 00000}. i. For all A, if binary A is regular, then so is unary A. ii. For all A, if unary A is regular, then so is binary A. One of the i and ii is true and other is false. Which is which? Give a proof and a counterexample.

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Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.