Past Question on Wilson's Theorem

Thanks Mathcad. I get the idea now.

One last attempt at posting this.The software on this system is hopeless.

We can write 36x27!+25 as (36x31!+(31x30x29x28)x25)/31x30x29x28 and can now factor out 31 from the numerator.So the expression is divisible by 31 and we can write

36x27!+25=31n for some n.

then,to use Wilson,we can write 36x27!+25=31!n/30!   and since 31!=30mod 31 ,rearrange to get

n=30!(36x27!+25)/30modulo31  which is divisible by 31.

hope this helps.

Thanks Mathcad, that looks interesting :)

Mathcad, I have transfered your answer over onto the original thread.

Badinage has asked the question exactly as I have requested but it is better if the answers are all together on the original thread. 

Thank you