Question

If p,q and r are prime numbers such that r=q+2 and q=p+2, then the number of triplets of the form (p,q,r) is _______

Answer 1

Answer:

As per given conditions

If p = x

Then , q = x+2

& r = x+4

So, now p, q, r are x, (x+2), (x+4) respectively.

=> this triplet is prime in Arithmetic progression… & such prime numbers are sequence of 3 prime numbers, which are consecutive terms in an AP.

& these terms are given by…

Tn = 3 + d*n , where d is common difference & n= {0,1,2 }

Since, in AP x, (x+2), (x+4) common difference = 2, So, terms are

3 + 2*0 = 3

3 + 2*1 = 5

3 + 2*2 = 7

So, required triplet is {3, 5, 7} . . . . . . . . Ans

Another example… { 3, 7, 11 )

3 + 4*0 = 3

3 + 4*1 = 7

3 + 4*2 = 11

Next example . . . . { 3, 11, 19}

3 + 8 * 0 = 3

3 + 8*1 = 11

3 + 8 * 2 = 19

Here, required answer . . P= 3, q = 5, r= 7

plz mark as brainliest

Step-by-step explanation: