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**Using the Euclidean algorithm.....I think...**

find the smallest natural number x such that 24x leaves a remainder of 2 upon division by 59

SO it seems to me that the way to approach this would be through the euclidean algorithm and a diophantine equation. Thinking about it for a moment would I perhaps set it up like this?

24x + 59y = 2

then proceed with the process?