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Junior Regional Olympiad - FBH 2017 Grade 8 Problem 4

Source:

September 20, 2018
statementsdivisibleprime

Problem Statement

Let nn and kk be positive integers for which we have 44 statements: i)i) n+1n+1 is divisible with kk ii)ii) n=2k+5n=2k+5 iii)iii) n+kn+k is divisible with 33 iv)iv) n+7kn+7k is prime Determine all possible values for nn and kk, if out of the 44 statements, three of them are true and one is false
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