12 Dec
2012
12 Dec
'12
10:28 p.m.
On Wed, Dec 12, 2012 at 10:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Just wrote a little program and ran it on numbers <= 1000, to get:
<< 9^3 + 10^3 = 12^3 + 1
64^3 + 94^3 = 103^3 + 1
73^3 + 144^3 = 150^3 + 1
135^3 + 235^3 = 249^3 + 1
244^3 + 729^3 = 738^3 + 1
334^3 + 438^3 = 495^3 + 1
Seeing that some of the solutions contain already perfect squares or prime powers, you could also ask about the solutions of the kind p^6 + y^3 = z^3+1 (example Ramanujan) x^18 + y^3 = z^3+ 1 (example 64,94,103 or 729,244,738) and other variants. Olivier