MathDB

It is said that a positive integer is not GOOD, if there exists a permutation of the integers from 1 to n,

(a_1,a_2,...,a_n)

such that

k + a_k

is a perfect square for all

k

. For example

5

is a GOOD number, since the permutation

(3,2,1,5,4)

checks the condition:

1 + 3 = 2^2

2 + 2 = 2^2

3 + 1 = 2^2

;

4 + 5 = 3^2

and

5 +4 = 3^2

. Find all GOOD numbers up to

12

Problem Statement