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3^(6) - 1^(6) = 12^(3) - 10^(3)
i.e. a^(2n) - b^(2n) = c^(n) - d^(n)
Give more examples of this(a & b must not have a common factor between them).

2006-10-16 02:33:56 · 3 answers · asked by rajesh bhowmick 2 in Science & Mathematics Mathematics

3 answers

3^4 - 2^4 = 9^2 - 4^2

5^4 - 2^4 = 25^2 - 4^2

7^4 - 2^4 = 49^2 - 4^2

Many more can be build up in such way.
Observe: a^2 = c, b^2 = d

2006-10-16 03:04:22 · answer #1 · answered by psbhowmick 6 · 2 0

a^(2n) is the same as (a^2)^(n)... so, what you have is:

(a^2)^(n) - (b^2)^(n) = c^(n) - d^(n)

So, you could say that any two values of a and b could work, if c=a^2 and d=b^2, since:
a^(2n) - b^(2n) = (a^2)^(n) - (b^2)^(n)

... but I don't think that's what you're looking for.

I'm not sure what sort of examples you are looking for, though. Other values for a/b/c/d with the same n? Other values of n? There would seem to be many possible solutions... I'd suggest writing a computer program to generate them.

2006-10-16 10:00:31 · answer #2 · answered by PM 3 · 0 0

hmmmmmmmmmmmmmmmmm

2006-10-16 09:35:10 · answer #3 · answered by simon_sez28 2 · 0 1

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