Question 1148790
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<pre>
Let "x" be the EVEN integer number exactly between the two unknown consecutive unknown integer numbers.


Then the unknown odd integer numbers are (x-1) and (x+1),

and the problem says that


    {{{(x-1)^2}}} + {{{(x+1)^2}}} = 802.

Then

    {{{x^2 - 2x + 1}}} + {{{x^2 + 2x + 1}}} = 802

    {{{2x^2}}} + 2 = 802

    {{{2x^2}}} = 800

    {{{x^2}}} = 800/2 = 400

    x = +/- {{{sqrt(400)}}} = +/- 20.


Thus, there are two pairs of consecutive integer numbers satisfying the condition.


One pair is (19,21),  The other pair is (-21,-19).    <U>ANSWER</U>
</pre>

Solved.