by Paul Táctico
Last Updated May 16, 2019 06:20 AM

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.$

Updated October 05, 2017 21:20 PM

Updated September 21, 2017 16:20 PM

Updated September 21, 2017 22:20 PM

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