SOLUTION: For any three consecutive numbers prove algebraically that the largest number and the smaller number are factors of the number that is one less than the square of the middle number

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Question 1106714: For any three consecutive numbers prove algebraically that the largest number and the smaller number are factors of the number that is one less than the square of the middle number.
Found 2 solutions by dkppathak, josgarithmetic:
Answer by dkppathak(439) About Me  (Show Source):
You can put this solution on YOUR website!
For any three consecutive numbers prove algebraically that the largest number and the smaller number are factors of the number that is one less than the square of the middle number.
let numbers are x x+1 x+2
we have to prove that
x(x+2)=(x+1)^2 -1 by solving Rhs
(x+1)^2 -1
X^2 +2x+1-1
x^2+2x
x(X+2)
proved (x+1)^2 -1=x(x+2)

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Start with integers n, n+1, n+2.

The description suggests n%28n%2B2%29=%28n%2B1%29%5E2-1.
Will this by itself work?

n%28n%2B2%29=%28n%2B1%29%5E2-1
Working with the right-side member,
%28n%2B1-1%29%28n%2B1%2B1%29
%28n%2B0%29%28n%2B2%29
n%28n%2B2%29-------same as the left side member.