Close Enough

Close Enough

Moderate
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Außer wenn die Primfaktoren von a, b bereits zusammenarbeiten, diktiert die eiserne Hand von Fundamental Theorem of Arithmetic, dass die ganzzahligen Potenzen a**pa und b**pb für zwei beliebige positive ganzzahlige Exponenten pa und pb niemals gleich sein können. Im heiteren Geist von “close enough for government work” definieren wir jedoch, dass zwei solche Potenzen "treffen", wenn ihre Differenz abs(a**pa-b**pb) multipliziert mit tolerance höchstens gleich der kleineren dieser Potenzen ist. (Diese Definition vermeidet absichtlich die Division, damit sie sowohl schnell als auch genau für beliebig große ganze Zahlen ist.) Zum Beispiel erwartet tolerance=100, dass a**pa und b**pb innerhalb von 1 % liegen.

Für gegebene positive ganze Zahlen gibt a, b die kleinsten positiven ganzzahligen Exponenten zurück (pa, pb) zurück, die die Anforderung von tolerance erfüllen.

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