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Discussion of Problem 1118. Nontrivial Numbers

a bit incorrect task
Posted by Grab 10 Feb 2006 12:06
In the task of problem #1118 the triviality(1) was not defined.
test #4 has 1 as i.
after putting triviality(1) be equal to 0, i've gotten AC.
So, in my opinion, this moment should be fixed in the task.

P.S.
sorry for my bad English
Re: a bit incorrect task
Posted by Ayhan Aliyev [BOTL] 10 Feb 2006 13:12
Yes I agree with you. Problem definition is unclear.
Re: a bit incorrect task
Posted by Vladimir Yakovlev (USU) 10 Feb 2006 14:12
Citation from problem statement:
Recall that a proper divisor of a natural number is the divisor that is strictly less than the number.
So, 1 has no proper divisors and its sum equals to 0. Hence, triviality of 1 equals to 0.
Re: a bit incorrect task
Posted by Grab 10 Feb 2006 19:59
Vladimir Yakovlev (USU) wrote 10 February 2006 14:12
Citation from problem statement:
Recall that a proper divisor of a natural number is the divisor that is strictly less than the number.
So, 1 has no proper divisors and its sum equals to 0. Hence, triviality of 1 equals to 0.

Sorry, but I do not agree with you.
0 is less then 1, but it is not its divisor.
So, we have a sutuation: there's NO divisor (that's why the sum is not 0, but it doesn't exist), strictly the function doesn't have any value at 1 (т.е. функция не определена в точке 1), but nil is a number and the condition Triv(1)=0 means it has it!
that what wanted to say.

P.S.
sorry for using Russian, but I really do not know how to explain my think in English

Edited by author 10.02.2006 20:00

Edited by author 10.02.2006 20:20
Re: a bit incorrect task
Posted by Vladimir Yakovlev (USU) 11 Feb 2006 03:23
In maths the sum of empty set of numbers is traditionally considered to be equal to zero.