2023/018) Can the sum of three squares of odd numbers be a perfect square

An odd number is of the form 2n+ 1, so let 3 odd numbers be 2a+1, 2b+1,2c+ 1

Now $(2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2+ a) + 1$

$(2b+1)^2 = 4b^2 + 4b + 1 = 4(b^2+ b) + 1$

$(2c+1)^2 = 4c^2 + 4c + 1 = 4(c^2+ c) + 1$

We observe that square of an odd is of the from 4n + 1

Now $(2a+1)^2 + (2b+1)^2 + (2c + 1)^4 = 4(a^2 + a + b^2 + b + c^2 + c) + 3$

Above is an odd number and of the form 4n + 3 so cannot be a perfect square 

So the answer is No