Question 47
Let $a$, $b$, $n$ be positive integers such that:
(i) $a^{2021} \mid n$ and $b^{2021} \mid n$
(ii) $2022 \mid a - b$ and $a \gt b$.
Prove that there is a subset of the divisors of the number $n$ having sum of elements divisible by $2022$ but not by $2022^2$.
(i) $a^{2021} \mid n$ and $b^{2021} \mid n$
(ii) $2022 \mid a - b$ and $a \gt b$.
Prove that there is a subset of the divisors of the number $n$ having sum of elements divisible by $2022$ but not by $2022^2$.