Question

Sa se arate ca:

13 | a
a= $5^{n} * 4^{n+3}+ 5^{n+1} * 4^{n+2} + 5^{n+3} * 4^{n} - 5^{n+2} * 4^{n+1}$
Oricare ar fi n∈N.

Answer 1

a=5^n*4^n(4^3 + 5*4^2 + 5^3 - 5^2*4)=
= 20^n(64+80+125-100)=20^n*169=20^n*13^2
 ⇒ 13| a pt ca a este multiplu al nr 13