Problem

Source: CWMI 2018 Q3

Tags: combinatorics, number theory



Let $M = \{1,2,\cdots , 10\}$, and let $T$ be a set of 2-element subsets of $M$. For any two different elements $\{a,b\}, \{x,y\}$ in $T$, the integer $(ax+by)(ay+bx)$ is not divisible by 11. Find the maximum size of $T$.