Chinese Remainder / Linear Congruences Ladder¶
Who This Is For¶
Use this ladder when you are comfortable with modular arithmetic basics, but statements that combine several residue conditions still feel slippery.
Warm-Up¶
- gcd and lcm
- extended Euclid / Bézout coefficients
- modular normalization into
[0, m)
Core¶
- merge two congruences into one equivalent congruence
- detect impossible systems with the gcd-consistency check
- solve one linear congruence by reducing to extended Euclid, even if the exact starter here focuses on system merges
Stretch¶
- explain why coprime CRT is only the clean theorem case, not the whole contest lane
- compare one composite-mod inverse with a full congruence-system merge
- compare pairwise merge against richer reconstruction techniques like Garner
Retrieval Layer¶
- exact starter -> chinese-remainder.cpp for congruence merges
- quick reminder sheet -> Chinese Remainder hot sheet
- compare-point doorway for one
a x ≡ b (mod m)equation -> extended-gcd-diophantine.cpp
Repo Anchors¶
Exit Criteria¶
You are ready to move on when you can:
- merge two congruences without guessing the algebra
- explain exactly when a non-coprime system is inconsistent
- reduce
a x ≡ b (mod m)to the same extended-Euclid worldview - decide when the task is only one inverse and does not need a full CRT merge