• i. Modular Arithmetic: Work in ${\mathbb{Z}}_m$:
• ii. Barrett and Montgomery Reduction: % by a run-time divisor costs 20–90 cycles; the compiler only turns division by a compile-time constant into multiplications.
• iii. Probability and Expectation: Almost every expectation problem is solved by one of:
• iv. Contest Mathematics: The math that contest problems assume without naming it.