ক্ষুদ্রতম সংখ্যা
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
সবচেয়ে ক্ষুদ্রতম সংখ্যা নির্ণয় কর যাকে মোট 24 টি সংখ্যা দিয়ে নিঃশেষে ভাগ করা যায়।
Re: ক্ষুদ্রতম সংখ্যা
if u mean positive integer,then it is 24!
- nafistiham
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Re: ক্ষুদ্রতম সংখ্যা
my smallest answer till now is $420$
the divisors are $1,2,3,4,5,84,6,7,10,12,14,15,20,21,28,30,35,42,60,70,105,70,210,420$
there are $26$ divisors
but, i think there is a smaller number.
the divisors are $1,2,3,4,5,84,6,7,10,12,14,15,20,21,28,30,35,42,60,70,105,70,210,420$
there are $26$ divisors
but, i think there is a smaller number.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: ক্ষুদ্রতম সংখ্যা
i have got the exact answer:-)it is 360 whose prime factorization is 2^3*3^2*5 which ensures its minimality.
Re: ক্ষুদ্রতম সংখ্যা
Yes, the right answer is $360$. Because 2,3,5 are the lowest prime numbers. Now use Divisor Function
If have the book Theory Of Numbers ---- by John e couri and Andrew adlar then see the book. Or without having book you can see this link. I think this is also useful for you.
http://mathschallenge.net/library/numbe ... f_divisors
If have the book Theory Of Numbers ---- by John e couri and Andrew adlar then see the book. Or without having book you can see this link. I think this is also useful for you.
http://mathschallenge.net/library/numbe ... f_divisors
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Re: ক্ষুদ্রতম সংখ্যা
I admit that the right ans is 360.But it can be more less like -360.It also have 24 divisors.Isn't it correct. Give me advice if I am wrong
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Re: ক্ষুদ্রতম সংখ্যা
If you consider negative integers,then you must count negative factors.Then actually there will be 48 factors,not 24.
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