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Part of 2017 India PRMO

Problems(1)

Algebra and number theory

Source: PRMO 2017

p,q

be prime numbers such that

n^{3pq}-n

is a multiple of

3pq

for all positive integers

n

. Find the least possible value of

p+q

number theoryprime numbersFermat Pseudo-PrimesPRMOEuler s Theoremcarmichael s number