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Prime number property

+1
71
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+41

(a^(n)b - ab^(n))/(2n)

When a and b are integers, and when the result is an integer too, i predict n is a prime number.

How can I prove it?

EDIT:

a and b mustn’t be equal to n and n mustn’t be 2.

lolomine09  Jan 24, 2018
edited by lolomine09  Jan 24, 2018
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#1
+26470
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"(a^(n)b - ab^(n))/(2n)

When a and b are integers, and when the result is an integer too, i predict n is a prime number."

Hmmm!

a = 4, b = 2, n = 4 gives (anb - abn)/(2n) = 56

a, b and (anb - abn)/(2n) are all integers, but n isn't prime.

Alan  Jan 24, 2018
edited by Alan  Jan 24, 2018
#2
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Indeed

Then

a and b must not be equal to n.

lolomine09  Jan 24, 2018
#3
+26470
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You’ll need tighter constraints than that!

With a = 4, b = 2, n = 8, the result is 8128.  n still not prime.

Alan  Jan 24, 2018

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