IIT JEE , AIEEE Forum - Mathematics , Algebra - How to prove that 18!+1 is divisible by 23?

nadeemoidu

First of all, this method of proving divisibilty problems does not come under jee syllabus. but it is useful for olympiads

a=b( mod n) means that a and b both leave the same remainder on dividing by n.
It is to be read as a is congruent to b modulo n.
So a=0(mod n) means that a is divisible by n.

it is a useful notation as we can use many properties like
a=b( mod n) and c = d( mod n)
implies that

a+c=b+d(mod n)

ac=bd( mod n)

a^p = b^p ( mod n)
and so on.

Also there are some little more complicated theorems like as siddarth said
Wilson's theorem states that (p-1)! +1 = 0( mod p) for all prime p.

My advise is that dont concentrate on this as it is not in the JEE syllabus. JEE divisibility questions are usually linked to binomial theorem

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