2 ms·
On the positive side, in integers modulo 3, we have n³ = n so 1³ + 2³ = 0³
by Someone 3y ago
On the positive side, in integers modulo 3, we have
n³ = n
so
1³ + 2³ = 0³
- HelloNurse 3y agoPythagorean triples must be three nonzero numbers, and the exponent must be 2. If you are interested in other equations, don't call them the same way; and more importantly, while generalizing to other exponents and sums of more than two numbers is reasonable, allowing 0 makes the problem trivial because all powers of 0 are 0 and the sum of any number of zeros is 0.
- Someone 3y ago> If you are interested in other equations, don't call them the same way; I didn’t do that. I implicitly alluded to Fermat’s last theorem, expecting readers to pick that up. > because allowing 0 makes the problem trivial because all powers of 0 are 0 The example I gave isn’t trivial. The trivial ones are x³ + 0³ = x³ Also, nitpicking, not all powers of 0 are 0. The convention is that 0⁰ = 1 (https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero)