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

Let me give a trick. We have $N + 92 = 13k_1 + 104 = 13(k_1 + 8)$ and $N+92 = 11k_2 + 99 = 11(k_2 + 9)$.
Then, $N+92 = 11\times 13 k_3$ or $N = 143k_3 -92$ or $N=143k_4 + 51$.
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