C.16.IR:5.3 - Combining counter remainders

A device starts at zero, increments once per event and stores N modulo 16. No reset or missed event occurs. A supplied count bound is 0 ≤ N < 100. The stored value 5 permits:

N in {5,21,37,53,69,85}.

These six values come from N = 5 + 16*k with an integer k in the range allowed by the bound. They all satisfy the original operation. The reading settles N < 90, while N < 30 remains unresolved; 21 and 37 are witnesses.

Suppose a second counter starts at the same event boundary, sees every same event, and stores N modulo 17. It reports 4. Test the six candidates against this second relation: only N = 21 remains. The physical event correspondence and initialization make the mathematical intersection appropriate.

If the supplied bound is relaxed to N < 300, both 21 and 293 satisfy the two remainders. The earlier uniqueness conclusion therefore depended on the bound. If the counters cover different event intervals, use separate counts and recover the relation between them before combining their readings.