Suppose that one byte in a buffer covered by the Internet checksum algorithm needs to be decremented (e. g., a header hop count field).
Give an algorithm to compute the revised checksum without rescanning the entire buffer. Your algorithm should consider whether the byte in question is low order or high order.
You can assume that you are given n the original checksum, the position of the byte which is to be decremented and the value by which the byte will be decremented.

Write a program that begins by reading in a series of positive integers on a single line of input and then computes and prints the product of those integers. integers are accepted and multiplied until the user enters an integer less than 1. this final number is not part of the product. then, the program prints the product. if the first entered number is negative or 0, the program must print “bad input.” and terminate immediately. next, the program determines and prints the prime factorization of the product, listing the factors in increasing order. if a prime number is not a factor of the product, then it