Question 120
The positive integers $a, b, c, d$ satisfy
$$
(i) a + b + c + d = 2023
$$
$$
(ii) 2023 \mid ab - cd
$$
$$
(iii) 2023 \mid a^2 + b^2 + c^2 + d^2.
$$
Assuming that each of the numbers $a, b, c, d$ is divisible by 7, prove that each of the numbers $a, b, c, d$ is divisible by 17.
$$
(i) a + b + c + d = 2023
$$
$$
(ii) 2023 \mid ab - cd
$$
$$
(iii) 2023 \mid a^2 + b^2 + c^2 + d^2.
$$
Assuming that each of the numbers $a, b, c, d$ is divisible by 7, prove that each of the numbers $a, b, c, d$ is divisible by 17.