Friedman Number - Friedman Numbers Using Roman Numerals

Friedman Numbers Using Roman Numerals

In a trivial sense, all Roman numerals with more than one symbol are Friedman numbers. The expression is created by simply inserting + signs into the numeral, and occasionally the − sign with slight rearrangement of the order of the symbols.

But Erich Friedman and Robert Happelberg have done some research into Roman numeral Friedman numbers for which the expression uses some of the other operators. Their first discovery was the nice Friedman number 8, since VIII = (V - I) × II. They have also found many Roman numeral Friedman numbers for which the expression uses exponentiation, e.g., 256 since CCLVI = IVCC/L.

The difficulty of finding nontrivial Friedman numbers in Roman numerals increases not with the size of the number (as is the case with positional notation numbering systems) but with the numbers of symbols it has. So, for example, it is much tougher to figure out whether 147 (CXLVII) is a Friedman number in Roman numerals than it is to make the same determination for 1001 (MI). With Roman numerals, one can at least derive quite a few Friedman expressions from any new expression one discovers. Friedman and Happelberg have shown that any number ending in VIII is a Friedman number based on the expression given above, for instance.