IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

deep01

Let a_n=(111------1) this 1 is n times

(A) a₉₁₂ is not prime

(b)a₉₅₁ is not prime

(C) a₄₈₀ is not prime

(D) a₉₁ is not prime

sir pls answer my question and pls also give the proper explanation as i don't how to solve such types of question.

ankurgupta91

if An =(111111----1) where n denotes the no. of 1
nw if n is even
then , it is clearly seen that pair of two ones is divisible by 11
so the no .of ones is even v can make pair of two ones i.e it can be divisible by 11
thus A480 is not prime
nd A912 is not prime
hope u got it.....
thanks.........

frenied

well it shudnt be a951 as well.consider a951.sum of its digits=1+1+1......951 times i.e 951 which is divisible by 3 and hence the no. must also be divisible by 3.so that option is also eliminated.and as for a proper method even i dont know of a better one than option checking.

pratik17

i dont agree with frenied as An = 11111........ n times & not 1+1+1+........... n times. So A951 wont b equal to 951. it will b 11111.........951 times. But vot Ankur has suggested seems to b correct logically.

pratik17

Pls correct me if i am wrong.

frenied

im not saying that An=1+1+1.... im saying SUM OF DIGITS in An shud be equal to that that is iit should be 1+1+....n times-The SUM OF DIGITS which will be equal to n or 951 as the case requires.

amar.gupta

Dear,

Still there is not any claercut way to find and get a prime no. its still a mystery which is unsolved yet.

so for check whether a no is prime or not you have to follow the same traditional definition that it is divisible only by iself.

though by this option elimination technique you can get the ans.

as ankur and frenied had done for you.

so good work ankur and frenied.

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