# 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.

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

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

Consider the three consecutive numbers as $$x-1,x,x+1$$.

$(x-1)^2 + x^2 = (x+1)^2 x^2= 4x One answer for the equation is x=0 and the other is x=4. Two possible consecutive number sets solves the equation. -1,0,1 and 3,4,5. Since you are looking for non-null integers only 3,4,5 are the consecutive numbers that satisfy the equation.$

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