What is the positive integer?
: What is the positive integer?
When the positive integer is divided by each of the integer from 2 to 22 inclusive, the remainder is one less than the dividing integer. When the positive integer is divided by by 23 the remainder is 0. What is the smallest positive integer that qualifies?
The answer is 4655851199.
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1 solution
The LCM of the integers from 2 to 22 inclusive is 232792560. The remainder of that LCM divided by 23 is 15. The value of m such that 1 5 m − 1 m o d 2 3 = 0 is 20.The product of the LCM and 20 less 1 is 4655851199. 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 1 0 9 1 1 1 0 1 2 1 1 1 3 1 2 1 4 1 3 1 5 1 4 1 6 1 5 1 7 1 6 1 8 1 7 1 9 1 8 2 0 1 9 2 1 2 0 2 2 2 1 2 3 0