Problem #54
Find Tuples
Let S denote the set of all 6-tuples (X_{1}, X_{2}, X_{3}, X_{4}, X_{5}, X_{6}) of positive integers such that
X_{1}^2+X_{2}^2+X_{3}^2+X_{4}^2+X_{5}^2 = X_{6}^2
Consider the set T={X_{1}X_{2}X_{3}X_{4}X_{5}X_{6}:(X_{1},X_{2},X_{3},X_{4},X_{5},X_{6})⋲S}.
Find the HCF of all members of T.