Sherlock and The Beast

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    There is an alternative solution, but not so efficient (but still O(1) in spite of recursion) and not so elegant as the Diophantine equation. This is linear congruence equation: 5x = n (mod 3). You can solve it by means of the extended Euclidean algorithm. I am aware that this is like 'A sledgehammer to crack a nut', but fyi. Here you can practise with the linear congruence.