Problem

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Tags: number theory, Divisors



Find the least natural number $n$, which has at least 6 different divisors $1=d_1<d_2<d_3<d_4<d_5<d_6<...$, for which $d_3+d_4=d_5+6$ and $d_4+d_5=d_6+7$.