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Indonesian IMO TST 2010 Test 4 problem 1

Source:

January 8, 2011
algebrapolynomialnumber theoryrelatively primenumber theory proposed

Problem Statement

find all pairs of relatively prime natural numbers (m,n) (m,n) in such a way that there exists non constant polynomial f satisfying gcd(a+b+1,mf(a)+nf(b)>1 gcd(a+b+1, mf(a)+nf(b) > 1 for every natural numbers a a and b b
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