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Triples of primes with a divisibility property

Source: Czech-Polish-Slovak 2004 Q2

April 28, 2013
limitnumber theory unsolvednumber theory

Problem Statement

Show that for each natural number kk there exist only finitely many triples (p,q,r)(p, q, r) of distinct primes for which pp divides qrkqr-k, qq divides prkpr-k, and rr divides pqkpq - k.