15

Part of 2018 Hanoi Open Mathematics Competitions

Problems(2)

pq/(p + q)=(m^2 + 6)/(m + 1) diophantine (HOMC 2018 Ind. p15)

Source:

Find all pairs of prime numbers

(p,q)

such that for each pair

(p,q)

, there is a positive integer m satisfying

\frac{pq}{p + q}=\frac{m^2 + 6}{m + 1}

Diophantine equationnumber theory

n lines on plane such every line intersects 12 (HOMC 2018 ind. sen15)

Source:

n

distinct straight lines on a plane such that every line intersects exactly

12

others. Determine all the possible values of

n

combinatorial geometrycombinatorics