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p x q x s(r) = p x s(q) x r = s (p) x q x r, 2 digits numbers, s= sum of digits

Source: 2021 Czech-Polish-Slovak Match Junior, team p6 CPSJ

September 12, 2021
number theorysum of digits

Problem Statement

Let s(n)s (n) denote the sum of digits of a positive integer nn. Using six different digits, we formed three 2-digits p,q,rp, q, r such that p⋅q⋅s(r)=p⋅s(q)⋅r=s(p)⋅q⋅r.p \cdot q \cdot s(r) = p\cdot s(q) \cdot r = s (p) \cdot q \cdot r. Find all such numbers p,q,rp, q, r.
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