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Show that 5^n is divisible by 4 (ie. prove [itex]5^n = 4x[/itex])

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...

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...

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