6 ^ n - 1 Es divisible entre 5?

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<img src="https://tex.z-dn.net/?f=%5Ctext%7BVeamos%20%3A%7D%20%5C%5C%5B2pt%5D%0A6%5E%7Bk%2B1%7D-1%3D6%5Ccdot6%5Ek-1%20%5C%5C%0A%5Chspace%2A%7B1.3cm%7D%3D%285%2B1%296%5Ek-1%20%5C%5C%0A%5Chspace%2A%7B1.3cm%7D%3D5%5Ccdot%206%5Ek%2B6%5Ek-1%20%5C%5C%0A%5Chspace%2A%7B1.3cm%7D%3D5%5Ccdot%206%5Ek%2B5p%20%5C%20%5C%20%2C%20%5C%20%20%5Ctext%7Bya%20que%20por%20hip%5C%27otesis%20%7D%20%5C%206%5Ek-1%3D5p%20%5C%5C%0A%5Chspace%2A%7B1.3cm%7D%3D5%286%5Ek%2Bp%29%5C%5C%0A%5Chspace%2A%7B1.3cm%7D%3D5p_1%20%5C%20%5C%20%2C%20%5C%20%5C%20%286%5Ek%2Bp%20%5Ctext%7B%20es%20un%20entero%29%7D%20%5C%5C%5B2pt%5D%0A%5Ctext%7BEntonces%20%7D%20%5C%206%5E%7Bk%2B1%7D-1%20%5C%20%20%5Ctext%7B%20es%20divisible%20por%205.%7D" />

<img src="https://tex.z-dn.net/?f=%5Ctext%7BPor%20lo%20tanto%20%7D%5C%206%5En-1%20%5C%20%5Ctext%7Bes%20divisible%20por%205%20%2C%20para%20todo%20%7Dn%20%5Ctext%7B%20natural%7D" />.