2019 is smallest no, sum of fourth powers of 5 int, sum of 6 consecutive
Source: 2019 Irish Mathematical Olympiad paper 2 p6
October 5, 2020
number theorySum of powersconsecutive
Problem Statement
The number has the following nice properties:
(a) It is the sum of the fourth powers of fuve distinct positive integers.
(b) It is the sum of six consecutive positive integers.
In fact,
(1)
(2)
Prove that is the smallest number that satis es both (a) and (b).
(You may assume that (1) and (2) are correct!)