Question  Consider the searching problem:  Input: A sequence of n numbers A = (a1, a2, a3, ….., an ) a value V.  Output: An index i such that v = A[i] or the special value NIL if v does not appear in A.  Write pseudocode for linear search, which scans through the sequence, looking for v. Using a  loop invariant, prove that your algorithm is correct. Make sure that your loop invariant fulfills  the three necessary properties.

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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.