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37(72 + 3x) = 14**45 , find integer x

Source: 2001 Estonia National Olympiad Final Round grade 9 p1

March 12, 2020
number theoryDigitsInteger

Problem Statement

John had to solve a math problem in the class. While cleaning the blackboard, he accidentally erased a part of his problem as well: the text that remained on board was 37⋅(72+3x)=14∗∗4537 \cdot(72 + 3x) = 14**45, where ∗* marks an erased digit. Show that John can still solve his problem, knowing that xx is an integer
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