Give a Prove that the only consecutive no nulls integers numbers a, b, c

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.



Answers 3


Assume the consecutive numbers to e $m-1$, $m$, and $m+1$. Substitute in the equation given, and you will get your answer.

Ishan Deo
Ishan Deo
May 16, 2019 06:15 AM

Hint: $c>a,b$ so, solve for $n$ in $n^2+(n+1)^2=(n+2)^2$.

tarit goswami
tarit goswami
May 16, 2019 06:16 AM

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.$

Vinanth S Bharadwaj
Vinanth S Bharadwaj
May 16, 2019 06:18 AM

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