Hints: 1999 ashme problem #25

Question

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819

4

+31

Please don't solve it, but give me a hint on what to do. My problem with these types of questions is my tendency to plug in random values.

1) I think that the denominators make this slightly complicated.

I am adding the question. Melody

Mathc1 Jan 10, 2020

edited by Melody Jan 10, 2020

Melody · Answer 1 · 2020-01-10T09:42:27

+118687

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What is the question ?

Melody Jan 10, 2020

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https://artofproblemsolving.com/wiki/index.php/1999_AHSME_Problems/Problem_25

Guest Jan 10, 2020

Guest · Answer 2 · 2020-01-10T09:42:57

Hint:

*Try getting rid of the denominators

*Use Wilson's Theorem

*Later use Division theorem

further hints:

It involves:

-mod.

-Factorials

Alan · Answer 3 · 2020-01-10T11:27:00

Since the answer is given along with the question I have solved it below, using a systematic approach (as I don't know what Wilson's theorem is!):