I realise there is a similar post however it doesn't help too much with my question as my primes are much larger.

The number n=3967703 is a product of two primes 1973 and 2011. Compute the least positive residue of 2^15mod(n) using the Chinese Remainder Theorem.

I have split it into two congruences

x=2^15(mod1973)

x=2^15(mod2011)

but I can't seem to solve it due to the large primes.

Thank you