Question

aratati ca numarul N=|1-a|+|1-2a|+|1-3a|+...+|1-50a| este divizibil cu 25, orice a>=1

Answer 1

Pentru orice a>=1, N=a-1+2a-1+3a-1+...+50a-1=a+2a+3a+...+50a-50=
a(1+2+3+...50)-50=a($\frac{50*51}{2}$)-50=a*25*51-50=25(a*51-2)