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easy divisibility including 7

Source: BiH JBMO TST 08 problem 2

June 1, 2008
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let x,y,z x,y,z be positive integers. If 7 7 divides (x\plus{}6y)(2x\plus{}5y)(3x\plus{}4y) than prove that 343 343 also divides it.