MathDB

a.) A 7-tuple

(a_1,a_2,a_3,a_4,b_1,b_2,b_3)

of pairwise distinct positive integers with no common factor is called a shy tuple if

a_1^2+a_2^2+a_3^2+a_4^2=b_1^2+b_2^2+b_3^2

and for all

1 \le i<j \le 4

and

1 \le k \le 3

a_i^2+a_j^2 \not= b_k^2

. Prove that there exists infinitely many shy tuples.
b.) Show that

2016

can be written as a sum of squares of four distinct natural numbers.

Problem Statement