# Math Help - Eulers Theorem problem

1. ## 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)

2. Not quite sure what you mean by Euler's Theorem is, but

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