Congruence Problem Examples

Number Theory · Axiom Academy

EXAMPLE Congruence Problem Examples Master fundamental congruence techniques through worked examples Excellent work! You have completed this congruence example. Here is what we learned: Modular Reduction: We can reduce bases and exponents modulo n to simplify calculations before computing large powers. Repeated Squaring: Break down large exponents by computing successive squares and combining them, which is far more efficient than direct multiplication. Multiplicative Property: The congruence relation preserves multiplication: if a ≡ b (mod n) and c ≡ d (mod n), then ac ≡ bd (mod n). Intermediate Reduction: Always reduce intermediate results modulo n to keep numbers manageable throughout the computation. These techniques are essential for solving congruence problems efficiently. Practice with different moduli and exponents to build mastery!

This is the written version of the interactive lesson above. See the full Number Theory course.