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Can you apply Fermat's last theorem here?
Over on "Homework help" someone posted this question ...
Prove that there are no integers a,b and c that satisfy this equation.
a^3 + b^3 = 7c^3 +3
Now this seems to me to be an extension of Fermat's Last Theorem in the case n=3. Or am I missing something really obvious?
This ones got me stumped!
1 Answer
- David ThorstadLv 68 years agoFavorite Answer
That's a really interesting thought. I tried to apply it for a few minutes and got stuck. It just not easy to go from the equation a^3 + b^3 = 7c^3 + 3 back to an equation with three integer cubes. Maybe it's doable, but I think you should stick with modular arithmetic, which gives a nice proof:
The cubes (mod 7) are 1 and 6. This equation says that a certain sum of two cubes is congruent to 3 (mod 7). But this is impossible, since none of 1+1, 1+6, 6+1, 6+6 is congruent to 3 (mod 7).
I hope this helps!
