Daniel J Smith Custom TMUA alpha · Question 5

Let $P(n)$ be a statement about integers with the following properties:

$P(1)$ and $P(2)$ are true;

for all $n\geq1$ the following statement is true: ( $P(n)$ and $P(n+1)$ ) is sufficient for $P(n+2)$

What is the strongest conclusion that necessarily follows?

P(n)

is true for all

n\geq1

P(n)

is true for all sufficiently large

n

, but not necessarily for all

n

P(n)

is true for infinitely many

n

, but not necessarily for all

n

P(n)

is true for all odd

n

but not necessarily for all even

n

P(n)

is true for all even

n

but not necessarily for all odd

n

FNo general conclusion can be drawn beyond

P(1)

and

P(2)

examday