MathDB

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Part of 2017 Czech-Polish-Slovak Junior Match

Problems(2)

max n, there is a_1a_2a_3...a_n divisible by a_2a_3...a_n}

Source: Czech-Polish-Slovak Junior Match 2017, individual p1 CPSJ

2/20/2020
Find the largest integer n≥3n \ge 3 for which there is a nn-digit number a1a2a3...an‾\overline{a_1a_2a_3...a_n} with non-zero digits a1,a2a_1, a_2 and ana_n, which is divisible by a2a3...an‾\overline{a_2a_3...a_n}.
number theorydivisibleDigitsmax
(p^2 + p) (q^2 + q) (r^2 + r) perfect square for p,q,r primes

Source: Czech-Polish-Slovak Junior Match 2017, Team p1 CPSJ

3/6/2020
Decide if there are primes p,q,rp, q, r such that (p2+p)(q2+q)(r2+r)(p^2 + p) (q^2 + q) (r^2 + r) is a square of an integer.
perfect cubenumber theoryprimes