Problem number 152
One of the most difficult tasks for me from more than 100 solved:
There are several ways to write the number 1/2 as the sum of inverse squares using different natural numbers.
For example, you can use {2,3,4,5,7,12,15,20,28,35}:
In fact, using only integers between 2 and 45 inclusive, there are only 3 possibilities to write 1/2. The remaining two are: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30 35,36,45}.
How many ways are there to write ½ as the sum of the inverse squares of different integers between 2 and 80 inclusive?
PS: I post 3 old translations from my blog at once, but I won't spam so ;-)
There are several ways to write the number 1/2 as the sum of inverse squares using different natural numbers.
For example, you can use {2,3,4,5,7,12,15,20,28,35}:
In fact, using only integers between 2 and 45 inclusive, there are only 3 possibilities to write 1/2. The remaining two are: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30 35,36,45}.
How many ways are there to write ½ as the sum of the inverse squares of different integers between 2 and 80 inclusive?
PS: I post 3 old translations from my blog at once, but I won't spam so ;-)
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Source: https://habr.com/ru/post/38839/
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