Determine the remainder when 1234567...404142 is divided by 43.

Start by expressing the number as (12345678*10^67) + (9*10^66 + 10*10^64 + 11*10^62 + ... + 41*10^2 + 42*10^0).

Now compute each part mod 43:

12345678 = 34 mod 43

10^67 = 24 mod 43

(9*99+1)*10^68 - 99*43 - 1 = 32*240 - 1 = 25 mod 43

99^2 = 40 mod 43

Then the AG sum is 25/40 mod 43, which is 6.

Finally 34*24+6 = 5 mod 43. The remainder of the number is **5**.