an easy one

Let p,q,r,be three prime numbers such that

5<=p<q<r
and
2p2-r2>=49
2q2-r2<=193

find p, q ,r

7 Answers

33
Abhishek Priyam ·

p=7
q=11
is one of the soln...

r=7

[6]but it soenot satisfies initial condition...

1
Rohan Ghosh ·

to find the three numbers you need to go methodically
then you will easily get the answer
the answer should satisfy initial conditions

1
pinky ·

p=17,q=19 & r=23

1
Rohan Ghosh ·

good work ,

but how do you know that this is the only possible combination?

1
ith_power ·

step1. prove that 2q2≤193++r2≤2p2+144. implying q2≤p2+72.
step2. 2p2≥49+r2>49+p2 implying p≥11.
step3. if p==11, r=13, not possible.
if p==13, r=17, not possible.
if p==17, we have found a solution.
let p>17 implying q>19 implying p+q>36 implying q2-p2>72 since q-p>2..
so p≤17. proved.

1
Rohan Ghosh ·

good proof ..
i proved the same way
i wonder if there is any other way to prove it..

1
rahul1993 Duggal ·

in the fourth line it is r>p and not p>r

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