Question

Show that the square of any integer is in the form of 4m+1

Answer 1

First of all the question will be : Show that the square of any integer is in the forn of 4m or 4m+1, where m is any integer.
Solution :-

We know that any positive integer can be of the form 4m or 4m + 1,
for some integer m.

Thus, anypositive integer can be of the form 4q or  4q + 1.

Thus we have

(4q)2 = 16q2 = 4(4q2) = 4m where m = 4q2

(4q+1)2 = 16q2 + 8q +1 = 4(4q2 +2q) +1 = 4m + 1 where m = 4q2 +2q.

∴ Square of any positive integer is of the form 4m or 4m+1, where m is any integer.
Hope it helps you...!