4 ms·
Another simple disproof: 3987 and 4365 are both divisible by 3 (and thus so is the left-hand side), but 4472 is not (and thus neither is the right-hand side, as
by Chinjut 12y ago
Another simple disproof: 3987 and 4365 are both divisible by 3 (and thus so is the left-hand side), but 4472 is not (and thus neither is the right-hand side, as 3 is prime).
- ggchappell 12y agoVery nice! Another easy one is looking at it modulo 4. The powers on the left-hand side are both odd perfect squares, which are thus 1 modulo 4. So their sum is 2 modulo 4. But the right-hand side is an even perfect square, which is 0 modulo 4. EDIT. I guess my modulo-100 discussion is really just a convoluted way of coming up with the above fact.
- Chinjut 12y agoSo it turns out not only could we ignore all but the last digits of the bases... we could furthermore ignore all but the last digits of the exponents!
- yen223 12y agoEasiest disproof: open a Python console and type in 3987**12 + 4365**12 - 4472**12 Arbitrary-precision integers FTW!