Question 89
All $p$ a prime number and $0 \leq a_{1}\lt a_{2}\lt \ldots\lt a_{m}\lt p$ şi $0 \leq b_{1}\lt b_{2}\lt \ldots\lt b_{n}\lt p$ some integers. We denote by $k$ the number of different debris I give $a_{i}+b_{j}, 1 \leq i \leq m, 1 \leq j \leq n$ When dividing with $p$. . Prove that:
a) if $m+n\gt p$, then $k=p$;
b) if $m+n \leq p$, then $k \geq m+n-1$.
a) if $m+n\gt p$, then $k=p$;
b) if $m+n \leq p$, then $k \geq m+n-1$.