Chinese Remainder Theorem

**knguyen2005** · March 23rd 2009, 10:08 AM

I forgot how to do the Chinese Remainder Theorem which applied for this question:

Calculate 45^35 modulo 13 given that
y === 3 mod 13
and y === 4 mod 45

Thanks

**ThePerfectHacker** · March 23rd 2009, 08:26 PM

Originally Posted by knguyen2005

y === 3 mod 13
and y === 4 mod 45

This is equivalent to, $y\equiv 3 + 7\cdot 13(\bmod 13)$ and $y\equiv 4 + 2\cdot 45(\bmod 45)$ .
Therefore, $y\equiv 94(\bmod 13)$ and $y\equiv 94(\bmod 45)$ . Thus, $y\equiv 94(\bmod 585)$ .

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