Modular Arithmetic Tracking
GMAT glossary · Playbook
Definition
Replace each quantity with its residue mod m, operate on residues, and reduce again.
Modular Arithmetic Tracking in plain English
Pull Modular Arithmetic Tracking when remainders repeat or you must track residues across operations. Clues include Remainder, congruent mod, leaves a remainder of, modulo. Blueprint: Replace each quantity with its residue mod m. Add and multiply residues, then reduce mod m again. Why it beats the long way: Carrying full integers is slower than carrying residues when only the remainder matters. Micro-example: What is 7^5 bmod 5? Residues: 7equiv 2, so track 2^5=32equiv 2 pmod5. Carry residues, not the full powers.
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