Hello, helloying!

There must be typos in the problem.

The claim is not true.

.[1]

. . . . . . . .

Prove by induction that: . .[2]

The recursion formula has a square root.

I don't see how the term could always be an integer.

In fact, we can't determine theterm of the sequence!second

In[1], let

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

In[2], let

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .