Start with the square numbers 1, 4, 9, 16, 25, 36, 45 49 and so on. Pick any other number and you can express it as a sum of squares.

For example :

2 = 1 + 1

34=1+4+4+9+16

101= 1+1+ 4+ 9+9+ 16+25+ 36

…and so on.

It’s not so difficult to agree with the statement as you could actually express any numbers as a sum of 1s (1+1+1+…..). So, what’s so special about this Quadratic Expressions?

Well, French mathematician Joseph-Louis Lagrange proved that every positive integer is either a square itself or the sum of two, three, or four squares. No more than four squares, x^2 + y^2 + z^2 + t^2, are ever needed to express any number, no matter how large.

Now that’s magic