Question 1: Multi-Property Number Analyzer

MathGenius educational platform wants to create a comprehensive number analysis tool that can identify various mathematical properties of numbers using string operations. Create a Java application to analyze numbers for multiple special properties.

Requirements:

• If the input number is not positive, print "<number> is an invalid number. Please enter a positive number"
• Check if the number is a Perfect Square (square root is a whole number)
• Check if the number is a Palindromic Number (reads same forwards and backwards)
• Check if the number is a Happy Number (sum of squares of digits eventually reaches 1)
• Check if the number is a Kaprekar Number (square can be split into two parts that sum to original)
• Display all properties found, or "No special properties found"

Sample Input/Output:

Enter the number
121
121 is a perfect square number
121 is a palindromic number
121 is a happy number
Special properties found: 3

Sample Input/Output 2:

Enter the number
-5
-5 is an invalid number. Please enter a positive number

Question 2: Digital Root and Property Calculator

NumberCrunch analytics company wants to analyze numbers for digital patterns and mathematical relationships. They need a system that processes numbers using string manipulation to find various digit-based properties.

Requirements:

• If number is not positive, print "<number> is invalid input"
• Calculate Digital Root (keep summing digits until single digit)
• Check if number is Neon Number (sum of digits of square equals original number)