Find the number of positive integers less than 101 that can not be written as the difference of two squares of integers.

Step-by-step solution

Let, c be positive integer 100 such that c ^2= a ^2- b ^2 ; a , b Z . C - I : Difference of a and b is 1 . array ll & 1^2-0^2=1 & 2^2-1^2=3 & 3^2-2^2=5 & 4^2-3^2=7 & 5^2-4^2=9 & & 50^2-49^2=99 array All odd number upto 100 can be expressed as difference of two squares. C - I I : Difference of a , b is 2 aligned & 2^2-0^2=4 & 3^2-1^2=8 & 4^2-2^2=12 & & 26^2-24^2=100 aligned All multiples of ' 4 ' upto 100 can be expressed as difference of two squares. C - III : Difference of a , b is 3 This case will give odd number