Let n be a positive integer, try to explain the reason why the power of N + 2 of 2 + 7 can be divided by 5

Let n be a positive integer, try to explain the reason why the power of N + 2 of 2 + 7 can be divided by 5

Using mathematical induction,
When n = 1,
The (n + 2) power of 2 + the (n + 2) power of 7 = 345 can be divided by 5,
Suppose that the proposition holds when n = k, that is, the (k Power) of 2 + the ((K + 2) power of 7 can be divided by 5,
Then, when n = K + 1, it has the (K + 1) power of 2 + the (K + 3) power of 7
=2 (the K power of 2 + the (K + 2) power of 7) + the (K + 2) power of 5 * 7
It is easy to know from the hypothesis that the formula can be divided by 5, so the proposition holds when n = K + 1
The above proposition is proved by mathematical induction