Given
; and
Where and are whole numbers. How many such exist so that the above conditions are satisfied.
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From the equations, x 2 = 2 x .
Moving the 2x to the other side, we get x 2 − 2 x = 0 .
Factoring, we get x ( x − 2 ) = 0 . This tells us x is either 0 or 2 (or both). When x=0, m=0. When x=2, m=4.
Thus, the answer is 2.