Defect Free System
A system of numbers in a given base is said to be Defect Free if there exists a one-one correspondence between that system and the decimal system. Is the system in base , where is a complex cube root of unity, defect free?
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1 solution
If we allow complex numbers in Base 10, then note that w 4 = w . This means that 10000 and 10 in Base w have the same complex representation in Base 10, so there cannot be a 1-to-1 correspondence.