Question 1189711
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Find the product of x•y, where x and y are positive integers and {{{0 = 3x^4 - x^3*y-9317}}}.
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<pre>
Given equation is equivalent to

    3x^4 - x^3*y = 9317,  

or

    x^3*(3x - y) = 9317.


Integer number 9317 has the primary decomposition  9317 = 7*11^3.


From uniqueness of prime decomposition for integer numbers, we conclude that  

    EITHER  x = 1,  3x-y = 9317  OR  x = 11 and  3*11 - y = 7;  y = 33-7 = 26.


First option produces negative value of y; therefore, we discard it.

The second option gives the <U>ANSWER</U> to the problem  x= 11, y = 26.


The requested product x*y = 11*26 = 286.    <U>ANSWER</U>
</pre>

Solved.