- #1
nomather1471
- 19
- 1
Show that ----> if n is even perfect number than n [tex]\equiv[/tex]6(mod10) or n[tex]\equiv[/tex]8(mod10)
nomather1471 said:I can't believe to myself i think i proved :)
http://www.loadtr.com/465992-mmmmm.htm
A perfect number is a positive integer that is equal to the sum of its proper divisors (positive divisors excluding the number itself). The first few perfect numbers are 6, 28, 496, and 8128.
Mod 10 is a mathematical operation that calculates the remainder when a number is divided by 10. Perfect numbers have a special property where their mod 10 value is always equivalent to 0 or 1.
This can be proven using the formula for perfect numbers: 2^(p-1) * (2^p - 1), where p is a prime number. By taking the mod 10 of this formula, we can show that the result will always be 0 or 1.
This proof helps us better understand the properties and patterns of perfect numbers. It also provides a more efficient method for identifying and generating perfect numbers, as we can use mod 10 to quickly check if a number is a perfect number or not.
Yes, there are other methods such as using the Euler's theorem or the Mersenne prime formula. However, proving it with mod 10 is a simpler and more straightforward approach that is widely used in mathematics.