1) is easy. The answer is $2020$ . For 2) , My solution: noticing that the elements in $X$ must be $ax^2+a^2x$ $(a=1,2,\dots,10, x\ge a)$ , so I just listed all the elements in $X$ (it took me nearly one hour in the exam ), then we easily get the answer $17$. By the way , I even haven't got a quicker solution after a week, it seems that maybe listing is the only solution....

RoinTnT wrote: 1) is easy. The answer is $2020$ . For 2) , My solution: noticing that the elements in $X$ must be $ax^2+a^2x$ $(a=1,2,\dots,10, x\ge a)$ , so I just listed all the elements in $X$ (it took me nearly one hour in the exam ), then we easily get the answer $17$. By the way , I even haven't got a quicker solution after a week, it seems that maybe listing is the only solution.... zhe standard answer considers the prime factors of a,b,tedious……（about 6 pages）