MathDB

Prove that there are infinitely many positive integers

m

for which there exists consecutive odd positive integers

p_m<q_m

such that

p_m^2+p_mq_m+q_m^2

and

p_m^2+m\cdot p_mq_m+q_m^2

are both perfect squares. If

m_1, m_2

are two positive integers satisfying this condition, then we have

p_{m_1}\neq p_{m_2}

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