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Equation in integers (Posted on 2020-12-06)

Determine all pairs of prime numbers (p, q) such that p² + 5pq + 4q² is the square of an integer.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

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computer exploration

| Comment 1 of 5

for p1=1:200

for p2=1:200

p=nthprime(p1);

q=nthprime(p2);

sq=p^2+5*p*q+4*q^2;

sr=sqrt(sq);

if round(sr)*round(sr)==sq

disp([nthprime(p1) nthprime(p2) sq sr])

end

finds only

     p     q  p^2+5*p*q+4*q^2   square
                                 root
     5    11        784           28
     7     5        324           18
    13     3        400           20

having checked primes up to the 200th, 1223.

Posted by Charlie on 2020-12-06 15:37:26

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