MathDB

4

Part of 2023 Francophone Mathematical Olympiad

Problems(2)

20n+2 divides 2023n+210

Source: P4 Francophone Math Olympiad Junior 2023

5/2/2023
Find all integers n⩾0n \geqslant 0 such that 20n+220n+2 divides 2023n+2102023n+210.
number theorydividesdivisible
a(a+1)(a+2) ...(a+2023) divides b(b+1)...(b+2023)

Source: P4 Francophone Math Olympiad Senior 2023

5/2/2023
Do there exist integers aa and bb such that none of the numbers a,a+1,…,a+2023,b,b+1,…,b+2023a,a+1,\ldots,a+2023,b,b+1,\ldots,b+2023 divides any of the 40474047 other numbers, but a(a+1)(a+2)⋯(a+2023)a(a+1)(a+2)\cdots(a+2023) divides b(b+1)⋯(b+2023)b(b+1)\cdots(b+2023)?
number theorydividesconsecutiveProduct