Question

1234567891011121314151617181920......424344 what is remainder when divided by 45?

Answer 1

it is not possible i hope you are interested

Answer 2

Consider that you can write the number in the following form:

1×10x1+2×10x2+...+43×10xn+44, where x1,x2,...,xn are positive integers.

Now, I will claim that for any positive integer k, 10k≡10(mod45).

Proof by induction: 101≡10, so it's true for the k=1 case. 10k+1=10k∗10≡10∗10=100≡10(mod45).

So now, 1×10x1+2×10x2+...+43×10xn+44 ≡(1+2+...+43)×10+44 =43×442∗10+44 =946×10+44≡9(mod45).

The answer is therefore 9.

Thus, it is the correct answer.