Question

Aratati ca exista numere naturale a,b,c,d astfel incat a³+b³+c³+d³ = 100¹⁰⁰​

Answer 1

Răspuns:

S=100^100=100×100^99=100×100^(3×33)=100×(100^33)^3=(1^3 +2^3+3^3+4^3)×(100^33)^3

=notam 100^33=x

S=(1*x) ^3 +(2x)^3 + (3x)^3 + (4x)^3 =a^3 +b^3 +c^3 +d^3