How many factors?

Level pending

Let $x$ be an even number. Suppose that the number $3^{x} + 1$ may be decomposed as follows:

$3^{x} + 1 = 2^{k} \times \varepsilon$

Where $\varepsilon$ is an odd number. What is the value of $k$ ?

The answer is 1.

1 solution

Porifera Ohm
Jan 12, 2015

X must be an even number so I try 3^2 + 1 = 10 2^1 × 5 = 10