Question 1170492
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(1)  Consider the statement "When y is divided by x the remainder is 29".


     It means that there is an integer number "n" such that

        y = nx + 29,   29 < x.         (1)



(2)  Consider next statement "When y is divided by x/2, the remainder is 13".


     It means that there is an integer number "m" such that

        y = {{{m*(x/2) + 13}}},   13 < {{{x/2}}}.     (2)



(3)  From equations (1) and (2)  we have

        nx + 29 = {{{m*(x/2) + 13}}},    x > 29   


     or, equivalently

        2nx + 58 = mx + 26,     x > 29

        58 - 26  = mx - 2nx,    x > 29

        32       = (m - 2n)x,   x > 29      (3)



(4)  Thus, the integer number  x  is a divisor of the number 32, and x > 29.


     But the only such integer is  x = 32.
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The problem is just solved, &nbsp;and the &nbsp;&nbsp;<U>ANSWER</U> &nbsp;is:  &nbsp;&nbsp;the number &nbsp;&nbsp;" x " &nbsp;&nbsp;is &nbsp;32.