Remainder Theorem & Modular Arithmeticशेषफल प्रमेय एवं मॉड्यूलर अंकगणित

Master polynomial and modular remainders, Fermat Little Theorem, Wilson Theorem, cyclicity of remainders, and large exponent remainders in CSAT.

Overview: Remainder Theorem & Modular Arithmetic अवलोकन: शेषफल प्रमेय एवं मॉड्यूलर अंकगणित

• Basic Division Algorithm: Dividend = (Divisor × Quotient) + Remainder (where 0 ≤ Remainder < Divisor).
• Modular Distributivity:
- (a + b) mod m = (a mod m + b mod m) mod m
- (a × b) mod m = [(a mod m) × (b mod m)] mod m
• Negative Remainder Concept: If remainder is -1 mod m, positive remainder = m - 1.
• Fermat's Little Theorem: If p is prime and a is not divisible by p, then a^p-1 ≡ 1 (mod p).

Essential Formula / Rule:
Dividend = (Divisor * Quotient) + Remainder | Fermat Little Theorem | Euler Totient