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Arithmetic Sequenceshard
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Consider three arithmetic progressions: A=1,4,7,10,dotsA = \\{1, 4, 7, 10, \\dots\\}A=1,4,7,10,dots B=2,7,12,17,dotsB = \\{2, 7, 12, 17, \\dots\\}B=2,7,12,17,dots C=3,10,17,24,dotsC = \\{3, 10, 17, 24, \\dots\\}C=3,10,17,24,dots How many positive integers less than or equal to 100010001000 are common to all three sequences?