Problems & Puzzles:
& 385, revisited.
March 12, 2018, Seiji Tomita posed the following puzzle:
generalizing the puzzle 104 and 385 as follows.
N = x1^n + x2^n +....+ xn^n,n>3.
N: Prime number
Each number is sum of nth power of its n sections where
the sections for each number can have distinct lengths.
For example, ABCD = A^4+B^4+C^4+D^4, ABCDE = A^5+B^5+C^5+D^5+E^5.
2230433 = 22^4 + 30^4 + 4^4 + 33^4
Q1: Find large
solutions for each nth power.
Q2: If possible, find the parametric solutions for each nth power.
Example for n=3, ((10^s-1)/3)^3+((2*10^s+1)/3)^3+1^3 =
Contributions came from Emmanuel Vantieghem
Here is my only result :
There are a few other numbers that satisfy the
first two conditions of the problem (for N= 5, 6 and 7)
but they are not prime.