# Tag Archives: 5-th Powers

## A^5 + B^5 + C^5 = D^5 + E^5 + F^5

## Solve A^5 – B^5 = C^3 – D^3 = E^2 – F^2 = N for positive integers

A,   B,   C,   D,   E,   F,   and   N   are positive integers   for example,     Find other solutions for   A < 100           … Continue reading

Posted in Number Puzzles | Tagged | 4 Comments

## N^5 = A^2 + B^2 for N ≤ 1000

and     are non-zero positive integers   multiplying both sides by   When is the sum of two squares a cube? https://benvitalenum3ers.wordpress.com/2015/05/06/when-is-the-sum-of-two-squares-a-cube/ multiplying both sides by     Solutions when   a = 1     … Continue reading

Posted in Uncategorized | Tagged , | 4 Comments

## Some patterns with Powers and factorials

Posted in Number Puzzles | Tagged , | 2 Comments

## Integers such that N^5 = A^5 + B^5 + C^5 + D^5 + E^5

(1)   A^5   =   B^5   +   C^5   +   D^5   +   E^5   +   F^5   For example,       72^5   =   67^5   +   47^5   … Continue reading

## Primes which are the reverse of a 5-th power

5-th Powers                             Prime numbers 2^5    =  32                                 … Continue reading

Posted in Math Beauty, Number Puzzles | Tagged , | 1 Comment

## A^5 + B^5 + C^5 = X^5 + Y^5 + Z^5 (Part 2)

A^5   +   B^5   +   C^5   =   X^5   +   Y^5   +   Z^5                                 A   +   B   +   C   =   X   +   … Continue reading

Posted in Number Puzzles | Tagged , | 1 Comment

## Prime numbers such that the sum of the digits raised to the 4th power is also a prime

The prime numbers under 1000 : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, … Continue reading