Math Ladders

These ladders cover arithmetic, number theory, and transform-based counting tools.

Two bridge chains are especially worth keeping explicit:

• Number theory basics -> GCD / LCM -> Chinese remainder / linear congruences
• FFT -> Polynomial / formal power series

Recommended Order

1. modular arithmetic
2. number theory basics
3. gcd / lcm constructions
4. chinese remainder / linear congruences
5. lucas theorem / large binomial mod prime
6. mobius and multiplicative counting
7. dirichlet convolution / prefix sums of number-theoretic functions
8. Min_25 / Du Jiao
9. linear recurrence / matrix exponentiation
10. berlekamp-massey / kitamasa
11. gaussian elimination / linear algebra
12. xor basis / linear basis
13. game theory / Sprague-Grundy
14. probability
15. BSGS / discrete log
16. modular square root / discrete root
17. primitive root
18. Pollard-Rho
19. FFT
20. polynomial / formal power series

Subtopic Ladders

• Modular arithmetic
• Number theory basics
• GCD / LCM
• BSGS / discrete log
• Modular square root / discrete root
• Primitive root
• Pollard-Rho
• Gaussian elimination / linear algebra
• Chinese remainder / linear congruences
• Lucas theorem / large binomial mod prime
• Mobius and multiplicative counting
• Dirichlet convolution / prefix sums of number-theoretic functions
• Min_25 / Du Jiao
• Linear recurrence / matrix exponentiation
• Berlekamp-Massey / Kitamasa
• XOR basis / linear basis
• Game theory / Sprague-Grundy
• Probability
• FFT
• Polynomial / formal power series

Representative Solved Notes

• Exponentiation
• Counting Divisors
• Throwing Dice
• K-th Term of Linearly Recurrent Sequence
• Common Divisors
• GCD on Blackboard
• CRYPTKEY
• General Chinese Remainder
• Discrete Logarithm Mod
• Sqrt Mod
• Primitive Root
• Factorize
• System of Linear Equations
• Binomial Coefficient (Prime Mod)
• Counting Coprime Pairs
• Sum of Divisors
• Sum of Totient Function
• XMAX
• S-Nim
• Dice Probability
• POST2
• Inv of Formal Power Series