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Quantitative Aptitude

Wilson's Theorem

If n=10000 ! ...

Question

If n = 10000! is divisible by $p^{p}$ where p is a prime number, what is the maximum value of p?

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Solution

The correct option is C 97
Option C is the correct answer. Check the video for the approach.

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Similar questions

Q. If

p

is a prime number, then

n^{p} - n

is divisible by

p

for all

n

, where

Q. If

P

is a prime number then

n^{p} - n

is divisible by

p

when

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Q. If

p

is a prime number,

x^{p} - x

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Q. Statement

1

:
If

p

is a prime number

(p \neq 2)

, then

[(2 + \sqrt{5})^{p}] - 2^{p + 1}

is always divisible by

p

(where

[.]

denotes the greatest integer function).

Statement

2

:
If

n

is a prime, then

^{n} C_{1},^{n} C_{2},^{n} C_{3}, \dots,^{n} C_{n - 1}

must be divisible by

n

Q. Assertion :The number

^{1000} C_{500}

is not divisible by

11

, because Reason: If

p

is a prime, the exponent of

p

n!

[\frac{n}{p}] + [\frac{n}{p^{2}}] + [\frac{n}{p^{3}}] + . . .

where

[x]

denotes the greatest integer

\leq x

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If n = 10000! is divisible by pp where p is a prime number, what is the maximum value of p?

The correct option is C 97Option C is the correct answer. Check the video for the approach.

If n = 10000! is divisible by $p^{p}$ where p is a prime number, what is the maximum value of p?

The correct option is C 97
Option C is the correct answer. Check the video for the approach.