Prove that the sum of an even integer and an odd integer is odd. Let n₁ be an even integer, and let n₂ be an odd integer. So n₁ = n₁ + n₂ = + 1 = for some integer k₂ and n₂ = (K₁ + K₂) + 1 is -Select-- for some integer k₂. Then

Flavius Josephus was a Jewish historian of the first century. Legend has it that hewas one of a group of 41 Jewish rebels who decided to kill themselves rather thansurrender to the Romans, who had them trapped. They decided to form a circle andto kill every third person until no one was left. Josephus, not wanting to die, calculated where he needed to stand so that he would be the last one aliveand thus would not have to die. Thus was born a class of problemsreferred to as the Josephus problem. These problems involve findingthe order of events when events in a list are not taken in order but,rather, they are taken every ith element in a cycle until none remains.For example, suppose that we have a list of seven elementsnumbered from 1 to 7:1 2 3 4 5 6 7If we were to remove every third element from the list, the first element to beremoved would be number 3, leaving the list1 2 4 5 6 7The next element to be removed would be number 6, leaving the list1 2 4 5 7 Demonstrates the use of an…

Here's some background information on our Gregorian calendar. Although the Gregoriancalendar was created in 1582, The United States did not adopt it until 1752. Therefore, theGregorian calendar formula for calculating leap years only applies to years 1752 and later in theUnited States. The Gregorian calendar provided an improved formula for calculating whichyears are Leap Years. The criteria for a determining whether a year is a Leap Year is:Leap Year Definition:• The year is evenly divisible by 4; • If the year can be evenly divided by 100, it is NOT a leap year, unless;• The year is also evenly divisible by 400. Then it is a leap year.Your assignment is to create a Python program that in general uses a function to determinewhether a year is a leap year and another function for obtaining year input values from the user.More specifically your program should:1. Contain a function that determines whether a year passed to it is:a. A valid year for the Gregorian calendar usage in the…

Determine the appropriate value for the decision parameter p to use in the Bresenham's circle drawing procedure. The instructions that Bresenham developed for drawing a circle are presented in this article in the form of an algorithm that may be followed step by step.