Close Enough

Close Enough


Z wyjątkiem sytuacji, gdy czynniki pierwsze a, b już współpracują, żelazna ręka Fundamental Theorem of Arithmetic dyktuje, że potęgi całkowite a**pa i b**pb nigdy nie mogą być równe dla dowolnych dwóch dodatnich wykładników całkowitych pa i pb. Jednak w jowialnym duchu “close enough for government work”, definiujemy dwie takie potęgi jako "trafione", jeśli ich różnica abs(a**pa-b**pb) pomnożona przez tolerance jest co najwyżej równa mniejszej z tych potęg. (Ta definicja celowo unika dzielenia, aby była zarówno szybka, jak i dokładna dla arbitralnie dużych liczb całkowitych) Na przykład, tolerance=100 oczekuje, że a**pa i b**pb będą w granicach 1%.

Dla podanych dodatnich liczb całkowitych a, b zwraca najmniejsze dodatnie wykładniki całkowite (pa, pb) które spełniają wymóg tolerance.

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