Question 102
A nonempty, finite set $A$ of positive integers is called quadratic if the sum of the elements of $A$ equals the square of the number of elements of $A$.
For example $A = \{1, 3, 4, 8\}$ is quadratic since $1 + 3 + 4 + 8 = 4^2$.
a) Give an example of a quadratic set with 20 elements.
b) Prove that every quadratic set contains at least one odd integer.
c) Prove that the intersection of two quadratic sets with the same number of elements is nonempty.
For example $A = \{1, 3, 4, 8\}$ is quadratic since $1 + 3 + 4 + 8 = 4^2$.
a) Give an example of a quadratic set with 20 elements.
b) Prove that every quadratic set contains at least one odd integer.
c) Prove that the intersection of two quadratic sets with the same number of elements is nonempty.