Represent as sum of squares

[MM]

Let M be natural number which is divisible by 4 and could be represented as a sum of three squares. Prove that M could be represented as a sum of four squares.

[broniran]

Let [tex]x^2+y^2+z^2=M[/tex].Obviously [tex]x,y,z[/tex]-even.So we can rewrite the equality: [tex]4a^2+4b^2+4c^2=M[/tex] which is equivalent to [tex]\sum_{cyc}(a+b-c)^2+(a+b+c)^2=M[/tex] Q.E.D