c - Integer arithmetic: Add 1 to UINT_MAX and divide by n without overflow -

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is there way compute result of ((uint_max+1)/x)*x-1 in c without resorting unsigned long (where x unsigned int)? (respective "without resorting unsigned long long" depending on architecture.)

it rather simple arithmetic:

((uint_max + 1) / x) * x - 1 = ((uint_max - x + x + 1) / x) * x - 1 =  ((uint_max - x + 1) / x + 1) * x - 1 = (uint_max - x + 1) / x) * x + (x - 1)

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