Give a Prove that the only consecutive no nulls integers numbers a, b, c that satisfy the equality $a² + b² = c²$. are 3, 4, 5. -Thank you in advance.
Assume the consecutive numbers to e $m-1$, $m$, and $m+1$. Substitute in the equation given, and you will get your answer.
Consider the three consecutive numbers as $x-1,x,x+1$.
$(x-1)^2 + x^2 = (x+1)^2 x^2= 4x
One answer for the equation is x=0 and the other is x=4. Two possible consecutive number sets solves the equation.
-1,0,1 and 3,4,5.
Since you are looking for non-null integers only 3,4,5 are the consecutive numbers that satisfy the equation.$