Question

What will be the remainder of if (16!+1) divided by 17?

Answer 1

Step-by-step explanation:

if p is a prime number, then (p-1)! +1 is a multiple of p ( by Wilson 's theorem)

so (17-1)! +1 will be divisible by 17

hence the remainder is 16.

Answer 2

Answer:

The remainder of (16!+1) divided by 17 is 0.

Step-by-step explanation:

To find the remainder of (16!+1) divided by 17, we can use Wilson's Theorem.

Wilson's Theorem states that if p is a prime number, then (p-1)! is congruent to -1 modulo p.

Using this theorem, we can simplify the expression as follows:

• Since 17 is a prime number, we can apply Wilson's Theorem to get (17-1)! congruent to -1 modulo 17.
• Simplifying (17-1)! gives us 16! congruent to -1 modulo 17.
• Adding 1 to both sides of the congruence, we get 16!+1 congruent to 0 modulo 17.

Therefore, the remainder of (16!+1) divided by 17 is 0.

By using Wilson's Theorem, we can determine that the remainder of (16!+1) divided by 17 is 0. This result can be obtained by simplifying (17-1)! and adding 1 to both sides of the congruence.

Learn more about Wilson's Theorem:

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