Y by
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 satises both (a) and (b).
(You may assume that (1) and (2) are correct!)

(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,


Prove that

(You may assume that (1) and (2) are correct!)