Question

Sa se arate ca $3^{2n-1}$ + $2^{n+1}$ divide 7,n e N*.

Answer 1

$3^{2n-1}+2^{n+1}$


Daca-i dam lui n valori, observam :
n=1=> 3¹+2²=7
n=2=>3³+2³=27+8=35=7*5
n=3=> 3⁵+2⁴=259=7*37
n=4=> 3⁷+2⁵=2219=7*317
n=5=> 3⁹+2⁶ =19747=7*2821

Se verifica divizibilitatea cu 7;