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Show that there is a digit unequal to 2

Source: VAIMO 2008, Problem 1

January 3, 2009
floor functionmodular arithmeticinequalities unsolvedinequalities

Problem Statement

Show that there is a digit unequal to 2 in the decimal represesentation of 33 \sqrt [3]{3} between the 1000000 1000000-th und 3141592 3141592-th position after decimal point.
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