(53*d) mod 3432=1, can be rewritten as 3432x+1 = 53*d where x is an integer Your answer depends on the allowed domain of d, does it it have to be an integer? Otherwise the solution is trivial and simply is a series of points given by d=(3432x+1)/53. If d is an integer, then since 53 is a prime number, you have to find d where 53d-1 contain factors 8⋅3⋅11⋅13. I do not think there is a closed form solution? – 2012-10-19
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You might want to have a look at the euclidean algorithm. – 2012-10-19