SOLUTION: I have been asked to "Show that if p is an odd number, then 4^3p + 1 is divisible by 5. (It is actually divisible by 65.) ) Where do I start?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have been asked to "Show that if p is an odd number, then 4^3p + 1 is divisible by 5. (It is actually divisible by 65.) ) Where do I start?      Log On


   

Question 75993: I have been asked to "Show that if p is an odd number, then 4^3p + 1 is divisible by 5. (It is actually divisible by 65.)
)
Where do I start?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
"Show that if p is an odd number, then 4^(3p) + 1 is divisible by 5.
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Since p is odd, let p=2n+1
Then you have 4^(6n+3)+1
=4^6n+4^3+1
=4^(6n)+49
=4096^n+49 for n=1,2,3...
Whole number powers of numbers that have a units digit of 6 will end in
a units digit of 6 ; When 49 is added the units digit will be 5 so
the number will be divisible by 5.
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Cheers,
Stan H.


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Cheers,
Stan H.