2

Part of 2004 Czech-Polish-Slovak Match

Problems(1)

Triples of primes with a divisibility property

Source: Czech-Polish-Slovak 2004 Q2

Show that for each natural number

k

there exist only finitely many triples

(p, q, r)

of distinct primes for which

p

qr-k

q

pr-k

r

pq - k

limitnumber theory unsolvednumber theory