# Eulers Theorem problem

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• December 14th 2009, 02:43 PM
ChrisBickle
Eulers Theorem problem
Heres the problem: Use Euler's Theorem or anything else needed to find the least positive x such that 2^(6073) is congruent to x(mod1023)
• December 14th 2009, 03:20 PM
chiph588@
Not quite sure what you mean by Euler's Theorem is, but

$2^{6073} = 2^{6070} \cdot 2^3 = (2^{10})^{607} \cdot 2^3 = 1024^{607} \cdot 2^3 \equiv 1^{607} \cdot 2^3 \equiv 8 \mod{1023}$.