Find My Pattern!
How many positive integers are there that are less than such that is divisible by ?
The answer is 2857.
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1 solution
Value of 2 x mod 7 repeats in a cycle of length 3. So clearly, the value of this expression only depends on value of x modulo 21. Easy to consider values mod 3 and 7 to check that the set of values in {1,21} that satisfy this condition are {2,4,5,6,10,15}. This works till 10000-10000%21 = 9996, giving 476*6 values. After that we have one more due to 9998 being = 2 mod 21.