- #1

- 785

- 15

## Homework Statement

1. Prove that 1111111......65 times is not a prime number.

2. If a,b,c,d are in GP , then (a

^{2}+b

^{2}+c

^{2})(b

^{2}+c

^{2}+d

^{2}) is :

(a) (ab+ac+bc)

^{2}

(b) (ac+cd+ad)

^{2}

(c) (ab+bc+cd)

^{2}

(d) None of the above

## Homework Equations

Formulas of GP :

1.S

_{n}= a(1-r

^{n})/(1-r)

2.a,b,c in GP , then b

^{2}=ac

3.a,b,c,d,e,....,z in GP , then

az=by=cx=dw =.....

4.T

_{n}= ar

^{n-1}

## The Attempt at a Solution

1. The number can be written as

N = 1+10 + 10

^{2 }+ 10

^{3}+.... + 10

^{64}

N= (10

^{65}-1)/9

Now how to proceed ?

2. Well I tried using b

^{2}=ac but to no avail.

Please help !!

Thanks in advance. :)