Remainder Theorems

Rarely Tested

Fermat's Theorem - For any integer $$a$$ and prime number $$p$$, $$a^p-a$$ is always divisible by $$p$$

Wilson's Theorem - For a prime $$p$$, remainder when $$(p-1)!$$ i divided by $$p$$ is $$(p-1)$$

Euler's Theorem - If M and N are co-prime to each other then the remainder when $$M^{\phi(N)}$$ is divided by N is 1

Formula Video


Question 1

Find the remainder when 65! Is divided by 67?

Question 2

Find the remainder when 16! + 86 is divided by 323

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Previous Year Stats

Remainder Theorems

1

question from CAT exam over the past 5 years

Formulas Asked Together in Previous Papers


Divisibility by different numbers

1 PYQ

HCF and LCM

1 PYQ

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