- #1
cscott
- 782
- 1
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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