Show that 5^n is divisible by 4 (ie. prove [itex]5^n = 4x[/itex])(adsbygoogle = window.adsbygoogle || []).push({});

The case for n = 1 works

For n = k + 1

[tex]5^{k+1} - 1 = 4x[/tex]

[tex]5^k \cdot 5 - 1 = 4x[/tex]

Then I can only see doing:

[tex]5(5^k - 1 + 1) - 1 = 4x[/tex]

and substituting in the case for n = k

[tex]5(4x + 1) - 1 = 4x[/tex]

But it doesn't work out...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof by Induction

**Physics Forums | Science Articles, Homework Help, Discussion**