Again separate the number into groups of two digits starting from the end. Taking the first group of digits add it to the tens of the following group and subtract twice of it from the units. For example, taking 35582, we have 3+5=8, 5-6=-1, 80-1=79. Taking 79 and 82, we have 79+8=87, 2-158=-156, 870-156=714. Taking 714, we get 7+1=8, 4-14=-10, 80-10=70. 70 is 1 modulo 23 so 35582 is 1 modulo 23. Sed intelligenti pauca.
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