SOLUTION: There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a reminder of 2 when divided by 4 leaves a remainder of 3 and so on until
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Question 1003340: There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a reminder of 2 when divided by 4 leaves a remainder of 3 and so on until 9. What is the number? Answer by ikleyn(52752) (Show Source):
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There is a number less than 3000 that when divided by 2 leaves a remainder of 1, when divided by 3 leaves a reminder of 2 when divided by 4 leaves a remainder of 3 and so on until 9. What is the number?
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Let N be that number.
Then N-1 is divisible by 2; is divisible by 3, is divisible by 4; is divisible by 5; and so on until 9.
Thus N-1 must be divisible by = 8*9*5*7 = 2520.
Now it is clear that the required number N less than 3000 does exist and is unique.
It is the number 2521.
