THE PYRAMIDAL WARING PROBLEM
A pyramidal number is a positive integer p of form p = (m3 - m)/6 for some m = 2.
The so- called pyramidal Waring conjecture is that any positive integer k can be represented as the sum of no more than five pyramidal integers (not necessarily distinct).
Write a Java program that, given as input an integer n, checks if the pyramidal Waring conjecture holds for all positive integers up to n.
Test your program for as large a value of n as possible within a time limit of no more than one hour: n = 103,104,105,106,..., and plot the running times (use log-scale if the running times are too discrepant).
What is the asymptotic complexity of your solution as a function of n?