Thursday

October 23, 2014

October 23, 2014

Posted by **Asad** on Saturday, March 14, 2009 at 5:41pm.

I am trying to prove that

x

r

= k

and k is a multiple of x only when x is prime.

I said that if x is non-prime, then:

Let a = 6

Let r = 4

6!

(6 – 4)! 4!

= 3(2) x 5 x 4!

(2!) 4!

= 15

It is not divisible by 6

My explanation is:

When a is a non-prime number, then a! is [a x (a-1) x (a-2)…x 2 x 1] and a divides out with at least one of the r and this makes it possible for k to be not divisible by x.

and when x is prime:

For example,

Let a = 7

Let r = 4

7!

(7 – 4)! 4!

= 7 x 6 x 5 x 4!

(3!) 4!

= 35

It is divisible by 7

My explanation is:

When a is a prime number, then a! is [a x (a-1) x (a-2)…x 2 x 1] and a does not divide out with any r and this makes it possible for k to be divisible by x.

I am sure there is an elegant wa to prove this; however, i dont exactly know how to do this...can u help plz?? i really appreciate it..thnx

**Answer this Question**

**Related Questions**

math - Let f:A->B, where A and B are nonempty, and let T1 and T2 be subsets ...

math - Is there a way to prove this in upwards of 5 steps? Apparently there is...

Geometry - Can you just help me with this thanks Directions: Tell which property...

College Math : Linear Algebra - Suppose A is a square matrix satisfying the ...

math - My math teacher wants us to prove that all of our answers are correct. ...

RESEARCH REPORT - HI I WOULD LIKE TO KNOW WHAT I CAN POSSIBLY PROVE ABOUT EITHER...

math - prove the following: given: ABCD is a trapezoid with bases BC and AD to ...

math - I need to prove my answer is correct, the directions say to simplify the ...

Math - Prove :cosx-cosy= -2sin(x+y/2)sin(x-y/2) Prove: 2cot-2tanx= 4-2sec^2x / ...

Algebra NEED HELP PLEASE - If x is the midpoint of line vy and wz And the prove ...