Comments on: A Number Theory Problem from the 43rd Tournament of Towns
https://blog.tanyakhovanova.com/2022/08/a-number-theory-problem-from-the-43rd-tournament-of-towns/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Fri, 16 Sep 2022 10:31:41 +0000
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By: Tanya Khovanova's Math Blog » Blog Archive » Three, Five, and Seven have Different Remainders When Divided by Three - New Marathi Live
https://blog.tanyakhovanova.com/2022/08/a-number-theory-problem-from-the-43rd-tournament-of-towns/#comment-13569
Fri, 16 Sep 2022 10:31:41 +0000https://blog.tanyakhovanova.com/?p=1671#comment-13569[…] There are many cute math problems that use the trivial fact announced in the title. For example, I recently posted the following problem from the 43rd Tournament of Towns. […]
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By: Tanya Khovanova's Math Blog » Blog Archive » Three, Five, and Seven have Different Remainders When Divided by Three
https://blog.tanyakhovanova.com/2022/08/a-number-theory-problem-from-the-43rd-tournament-of-towns/#comment-13539
Thu, 18 Aug 2022 15:12:33 +0000https://blog.tanyakhovanova.com/?p=1671#comment-13539[…] There are many cute math problems that use the trivial fact announced in the title. For example, I recently posted the following problem from the 43rd Tournament of Towns. […]
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By: Puzzled
https://blog.tanyakhovanova.com/2022/08/a-number-theory-problem-from-the-43rd-tournament-of-towns/#comment-13515
Thu, 04 Aug 2022 10:24:51 +0000https://blog.tanyakhovanova.com/?p=1671#comment-13515More accurately, we have three consecutive terms of an arithmetic progression with common difference 2. So exactly one of those is divisible by 3.
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By: Puzzled
https://blog.tanyakhovanova.com/2022/08/a-number-theory-problem-from-the-43rd-tournament-of-towns/#comment-13512
Wed, 03 Aug 2022 10:03:06 +0000https://blog.tanyakhovanova.com/?p=1671#comment-13512n-3, n-5, n-7 are all prime. But at least one of three consecutive terms of an arithmetic progression is divisible by three, so it must be exactly 3. And the largest candidate can be found from n-7=3. Since 10 satisfies the conditions it is the answer.
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