2023 IOQM/Problem 1
Revision as of 11:45, 26 September 2023 by Sansgankrsngupta (talk | contribs) (→Solution 1(Spacing of squares))
Problem
Let be a positive integer such that . Let be the number of integers in the set
. Let , and .
Find .
Solution 1(Spacing of squares)
If for any integer , if is an integer this means is a perfect square. Now the problem reduces to finding the difference between maximum and minimum no. of perfect squares between There are 1000 numbers here.
The idea is that for the same range of numbers, the no. of perfect squares becomes less when the numbers become larger for example, there are 3 perfect squares between 1 and 10 but none between 50 and 60.
So maximum value of occurs when is minimum and the minimum value of occurs when is maximum.
Minimum value of = 1