# Remainder Theorem for CAT PDF

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Remainder Theorem for CAT PDF consists of the remainder theorems useful for CAT and also questions on CAT remainder theorem. The Remainder theorems in CAT consists of questions on Wilson theorem, Chinese remainder theorem and Fermat’s little theorem.

You can see that many times questions are asked in CAT Previous question papers. Take a free CAT mock test to analyse your preparation level.

Remainder Theorems:

You can download the Remainder Theorem for CAT PDF or you can go through the short details below.

Fermat’s little theorem for CAT:

Fermat’s theorem is an important remainder theorem which can be used to find the remainder easily.

Fermat’s theorem states that for any integer ‘a’ and prime number ‘p’, ‘(a^p)-a’  is always divisible by ‘p’.

Euler’s Theorem for CAT:

Euler’s theorem is one of the most important remainder theorems.

Euler’s theorem states that a^[Ø(n)]  (mod n ) = 1 (mod n) if ‘a’ and ‘n’ are co-prime to each other.
So, if the given number ‘a’ and the divisor ‘n’ are co-prime to each other, we can use Euler’s theorem.

Chinese remainder theorem for CAT:

Chinese remainder theorem is useful when the divisor of any number is composite.

Let M be a number which is divided by a divisor N. The theorem states that if N is the divisor which can be expressed as N = a*b where a and b are co-prime

Then,

M mod N = ar2x + br1y

Here r1 = M mod a

And r2 = M mod b

Here, ax + by = 1

Thus, we can see that if we are aware of the Chinese remainder theorem then the seemingly difficult questions can be solved with ease. You can practice more such questions from our CAT Online Tests to master the topic.

You can download the CAT Maths formulas PDF for other Quant formulas for CAT.

Wilson’s Theorem for CAT:

According to Wilson’s theorem for prime number ‘p’,

[(p-1)! + 1] is divisible by p.

In other words, (p-1)! leaves a remainder of (p-1) when divided by p.

Thus, (p-1)! mod p = p-1

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