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> other times, a solution is known not to exist, as with all whole numbers that leave behind a remainder of 4 or 5 when divided by 9 Curious how we are able to
by nodesocket 8y ago
> other times, a solution is known not to exist, as with all whole numbers that leave behind a remainder of 4 or 5 when divided by 9
Curious how we are able to prove that and with certainty say this is a rule?
- mjcohen 8y agoOff the top of my head: the cubes of 0,1,2,3,4,5,6,7,8 mod 9 are 0,1,-1,0,1,-1,1,-1. The sums of three of these, mod 9, are 0, 1, 2, 3, -1, -2, -3 or 0, 1, 2, 3, 6, 7, 8, so the sum of 3 cubes can not be 4 or 5 mod 9.