Question

find the number of positive integer less than 101 that cannot be written aa difference of two squares of integers​

Answer 1

Answer:

Step-by-step explanation:

Notice that every odd number can be expressed as the difference of two squares: namely, 2n+1=(n+1)^2−n^2. Moreover, if m=4n, then m=(2n+1)+(2n−1), so m=(n+1)^2−(n−1)^2.

On the other hand, if m is 2 times an odd number, it cannot be expressed as a difference of squares: arguing mod 4, a^2−b^2 can only be equal to 0, 1 or −1, whereas m≡2 mod 4.

Hence the answer to your question is 25