محاولة صغيرة للمسألة العاشرة :

Find

Solution

Note that

where are primes

now, for all integers we have




so all will have exactly one in their prime factorization

now note also that



so all will have a in their prime factorization

also note that



so, at least on of the integers will not have a in its prime factorization and that's enough for us to exclude from the gcd

so, we conclude that



~ والله أعلم ~