[Solved] How to find the number of contiguous subsequences / subarrays whose product can be expressed as difference of squares of 2 random integers?


Any number can be represented as a difference of squares if it is odd, or a multiple of 4.
The problem arises when a product has only a single 2 in the prime factorisation. So we can mark them. (i.e all the 2)
Given this we can easily deduce that only what is not a valid subarray for the given condition is

[odd, 2, odd, 4*n, odd]
[0,   1,   2,    3,   4]

We can see that position 3 will not be in any of the valid subarrays so you can count odds on the left and on the right.
Number of subarrays where position 1 takes part
the non valid subarrays are [odd, 2], [2, odd], [2], [odd, 2, odd]

Subtracting 15 – 4, Hence the answer is 11.

Do this for every number that has a single two in its prime factorisation.

solved How to find the number of contiguous subsequences / subarrays whose product can be expressed as difference of squares of 2 random integers?