Prime Factors and Exponents!

[zpolin]

Hi, this problem has really stumped me and i hope someone can help:

[deleted by Stacey; please see below]

I started off (hopefully correctly) by reducing 4^17 to (2^2)^17 which gave me 2^34. However I must have gone wrong after this because I don't know what number you get when you subtract 2^34 - 2^28.

Thanks for your help!

[gokul_nair1984]

I started off (hopefully correctly) by reducing 4^17 to (2^2)^17 which gave me 2^34. However I must have gone wrong after this because I don't know what number you get when you subtract 2^34 - 2^28.

You are correct till this part:
(2)^34-(2)^28-----(1)

Now (2)^34 can be written as (2)^28 * (2)^6 by the property (x)^m * (x)^n= (x)^(m+n)

ie (1) reduces to (2)^28 * (2)^6 -(2)^28
Taking (2)^28 common, we get (2)^28[(2)^6 -1)]
or (2)^28[(64 -1)] = (2)^28 *63.

The greatest prime factor can be obtained by rewriting 63 as 7*3*3. Thus greatest Prime factor is 7.

Hope this makes sense.

[StaceyKoprince]

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