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Compute and reason with congruences modulo n

The learner can compute and reason with congruences modulo n. This capability is distinct from mere exposure to or isolated use of division algorithm; remainders.

3 published problems

1. The Ouroboros Binding — At an orchard ruin in Avelwythe, an ouroboros binding sends a never-ending menagerie through the lake mist. Determine whether its exact instruction point can ever repeat.
2. Four Ways Back to One — Complete Rook's split-dial record to uncover every position whose square returns to 1 on a fifteen-position dial.
3. The Same Equation, Different Worlds — Carry one familiar equation through three coherent folds of the Manyfold and discover which proof step depends on the surrounding mathematics.