Number Theory - Remainders A number is of the form $13k_1+12$ and of the form $11k_2+7$
That is $N = 13k_1 + 12 = 11k_2 + 7$
Now why must N also equal $(13 \times 11)k_3 + 51$ ?
Thanks

$N$ as defined is $12$ mod $13$ by first definition and $7$ mod $11$ by second definition, since both $13$ and $11$ are relatively prime (in fact primes) thus $N$ should have same mod ($13 \times 11$) as well, rest follows by manipulating the $12$, $7$ remainders with $13$, $11$
