# Math Help - Chinese Remainder Theorem

1. ## Chinese Remainder Theorem

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

2. 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, $y\equiv 94(\bmod 585)$.