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The solution is to find the least common multiple of 3,4,5,6,7 and 9. One more than any integral multiple of that number will meet the requirements.
Thus, LCM of 3,4,5,6,7,9 = 1260
so 1261, 2521, 3781 etc all will leave a remainder of 1 when divided by 3,4,5,6,7 and 9.
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