Remainder formula- Quant Study Notes for Competitive Exams

What is the formula for remainder and quotient?

Dividend ÷ Divisor = Quotient and Remainder

What Fermat's little theorem states?

It states that Remainder [N^{P – 1}/P] = 1 (where, P is a prime number and N < P) Or, Remainder [a^{P – 1}/P] = 1 [where, P is a prime number and HCF (a, P) = 1]

What is Wilson's theorem?

It says

1. Remainder [(P – 1)!/P] = -1 or (P – 1)

2. Remainder [(P – 2)!/P] = 1

3. Remainder [(P – 3)!/P] = (P – 1)/2

(Where P is a prime number)

What are the rules for numbers in the form of a ⁿ + bⁿ?

i) When n is odd, it is divisible by (a + b) ii) We can’t say anything when n is even.

What is the last two digits of the power of the number containing unit digit in base as 5?

→5

It has two cases, i) The power and the second last digit of base is odd ⇒ 75 ii) Otherwise ⇒25