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Kummer
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Show that for any n>1 we can construct a positive integer consisting of only 1's and 0's such that this integer is a multiple of n.
matt grime said:Interesting variation: show that if n is no divisbible by 2 or 5, then there you can choose this multiple to have precisely two 1s and the rest of the digits 0.
matt grime said:My special case was: if 10 and n are coprime, let r be the order of 10 in the units mod n, then 10^r-1 is divisble by n.
matt grime said:Kummer, I think you're under the mistake apprehension that we found your question hard...
A Fun Divisibility Problem is a mathematical puzzle that involves finding a number that is divisible by a specific set of numbers. These types of problems are often used as brain teasers and can vary in difficulty.
The key to solving a Fun Divisibility Problem is to find a number that is divisible by all the given numbers. This can be done by finding the common factors of the numbers and then finding the smallest number that contains all those factors. Another approach is to use divisibility rules for each number in the set.
Fun Divisibility Problems help improve mathematical skills such as problem-solving, critical thinking, and pattern recognition. They also help develop patience and perseverance when faced with challenging problems.
Yes, there are several strategies that can be used to solve Fun Divisibility Problems. These include prime factorization, divisibility rules, and finding the LCM (least common multiple) of the numbers. It is also helpful to break down the problem into smaller parts and work through them systematically.
While Fun Divisibility Problems may seem like purely abstract mathematical puzzles, they can have real-life applications. For example, they can be used in coding and programming to optimize algorithms or in cryptography to secure data. They can also be used in designing puzzles and games.