Is $5^{k - 5}$ a multiple of4??

Open in App

Solution

Let us assume that $5^{k} + 5$ is a multiple of 4.
$\Rightarrow 5^{k} + 5 = 4 t$
$\Rightarrow 5^{k} = 4 t - 5$ - - - (1)
Let's check if the same holds true for k + 1.
$5^{k + 1} + 5 = 5^{k} .5 + 5$
= (4t - 5) 5 + 5
= 20t - 25 + 5
= 20t - 20 = 4(5t - 5)
This means that $5^{k + 1} + 5$ is a multiple of 4.
Hence, our assumption was correct.

Suggest Corrections

Similar questions

Prove that $5^{k} - 5$ is multiple of 4

\frac{4}{(216)^{- \frac{2}{3}}} + \frac{1}{(256)^{- \frac{3}{4}}} + \frac{2}{(243)^{- \frac{1}{5}}}

4 + 3 x a n d 5 - 4 x + 2 x^{2}

3 x^{2} - 5 x a n d - x^{2} + 2 x + 5

O F_{4}

Which can't OF4 not exist theocratically?

Join BYJU'S Learning Program