# Proving Perfect Number Equivalency with Mod 10

• nomather1471
In summary, a perfect number is a positive integer that is equal to the sum of its proper divisors. Mod 10 is a mathematical operation that can be used to show the equivalency of perfect numbers. This can be proven by using the formula 2^(p-1) * (2^p - 1), where p is a prime number. The significance of this proof is that it helps us better understand the properties of perfect numbers and provides a more efficient method for identifying them. While there are other methods for proving this equivalency, using mod 10 is a simpler and more widely used approach.
nomather1471
Show that ----> if n is even perfect number than n $$\equiv$$6(mod10) or n$$\equiv$$8(mod10)

Do you know the Euclid-Euler form?

2^(p-1) *(2^p-1) formula i think you have said, i know this formula but i haven't get the result with this.

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I can't believe to myself i think i proved :)

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nomather1471 said:
I can't believe to myself i think i proved :)

yea. it should be it

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it is important point of exponential of 4 is congruence 4 or 6 mod 10, i have missed it i think :)

## 1. What is a perfect number?

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.

## 2. How does mod 10 relate to perfect numbers?

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.

## 3. How can we prove the equivalency of perfect numbers with mod 10?

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.

## 4. What is the significance of proving perfect number equivalency with mod 10?

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.

## 5. Are there any other methods for proving perfect number equivalency?

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.

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