Răspuns:
Explicație pas cu pas:
[tex]\bf 7^{n+3} + 3\cdot 7^{n+2}-13\cdot 7^{n +1} +7^n =[/tex]
[tex]\bf 7^n\cdot \big(7^{n+3-n} + 3\cdot 7^{n+2-n}-13\cdot 7^{n +1-n} +7^{n-n}\big) =[/tex]
[tex]\bf 7^n\cdot \big(7^{3} + 3\cdot 7^{2}-13\cdot 7^{1} +7^{0}\big) =[/tex]
[tex]\bf 7^n\cdot \big(343 + 3\cdot 49-13\cdot 7 +1\big) =[/tex]
[tex]\bf 7^n\cdot \big(343 + 147-91 +1\big) =[/tex]
[tex]\bf 7^n\cdot \big(490-91 +1\big) =[/tex]
[tex]\bf 7^n\cdot \big(399 +1\big) =[/tex]
[tex]\bf 7^n\cdot 400 = 7^n\cdot 20^2 =[/tex]
[tex]\bf 7^n\cdot 2^2\cdot 5^2[/tex] este divizibil cu 2; 4; 5; 10; 20; 7; 14; ....
