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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
4 years, 3 months ago

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

As such, the \(26\)th digit will be \(3\)

Aditya Parson - 4 years, 3 months ago

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now u give a question

Superman Son - 4 years, 3 months ago

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Sure.

Try this.

Aditya Parson - 4 years, 3 months ago

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

Tan Li Xuan - 4 years, 3 months ago

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I have seen this question before.....

Shourya Pandey - 4 years, 3 months ago

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yes it is a rmo question

Superman Son - 4 years, 3 months ago

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