# number theory marathon

lets start a number theory marathon..... QUESTION 1- N is a 50-digit number (in decimal representation). All digits except the 26th digit (from the left) are 1. If N is divisible by 13, find its 26-th digit.

Note by Superman Son
5 years, 2 months ago

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Hint: Note that $$111111 \equiv 0 \pmod{13}$$

As such, the $$26$$th digit will be $$3$$

- 5 years, 2 months ago

now u give a question

- 5 years, 2 months ago

Sure.

Try this.

- 5 years, 2 months ago

$$111111 \equiv 0 \pmod{13}$$ so the 26th digit is 3

- 5 years, 2 months ago

I have seen this question before.....

- 5 years, 2 months ago

yes it is a rmo question

- 5 years, 2 months ago