IIT JEE , AIEEE Forum - Mathematics , Algebra - prove that 96!/(48!)-1 is divisable by 97.

man111

(1) prove that 96!/(48!)-1 is divisable by 97.

sboosy

the pattern goes like this

(6!/3!)-1 is divisible by7

but (8!/4!)-1 is not divisible by 9

but again (10!/5!)-1 is divisible by 11

then u might say that id denominator is odd it works

but even that is wrong

because (14!/7!)not divisible by 15

as far as i know the conditions for such a divisibility are as follows

1.denominator should be odd.eg 6!/3!

2.the number with u divide should be prime

since in the question asked we have 48! in the dr.(48 being even)

it is not divisible

venky1907

sboosy,

that seems to be a brilliant way.... actually ,even i had the same idea...