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Topic: Proof requested
Replies: 1   Last Post: Jul 10, 1996 12:27 PM

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Pomeli Ghosh

Posts: 25
Registered: 12/12/04
Proof requested
Posted: Jul 9, 1996 10:52 PM
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Given: x,y and z are relatively prime integers each > 1
and p is a prime > 5.

Consider the following equations:

x^2 = y^p + 1 (1)
x^4 - y^4 = z^p (2)

Conjectures:
Equation (1) cannot have any rational solution
Equation (2) cannot have any integer solution

Any comment , reference or suggestion leading to a proof of each
conjecture shall be appreciated.

regards,
pomeli

PS: if you can also mail your response to me at pomeli@paul.rutgers.edu,
it'll be helpful as I don't read the newsgroup frequently







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