1p=17,q=19 & r=23
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
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7 Answers
33p=7
q=11
is one of the soln...
r=7
[6]but it soenot satisfies initial condition...
1to find the three numbers you need to go methodically
then you will easily get the answer
the answer should satisfy initial conditions
1good work ,
but how do you know that this is the only possible combination?
1step1. 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.
1good proof ..
i proved the same way
i wonder if there is any other way to prove it..
