Question

Aratati ca numarul B= 2ⁿ+3x7ⁿ+1+2ⁿ+2-2ⁿ+1x7n,este divizibil cu 250 pentru orice nr nat .

Answer 1

a=2^n*2^3*7^n*7+2^n*2^2*7^n*7^2-2^n*2*7^n=
= 2^n*7^n(2^3*7+2^2*7^2-2)=
=2^n*7^n(8*7+4*49-2)=
=2^n*7^n*250 care e divizibil cu 250 pt orice n nr natural