document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #620106 by ikleyn(52754)\"\" \"About 
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\n" ); document.write( "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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\n" ); document.write( "\n" ); document.write( "Let N be that number.\r
\n" ); document.write( "\n" ); document.write( "Then  N-1  is divisible by  2;  is divisible by  3,  is divisible by  4;  is divisible by  5;  and so on until  9.\r
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\n" ); document.write( "\n" ); document.write( "Thus  N-1  must be divisible by  \"2%5E3%2A3%5E2%2A5%2A7\" = 8*9*5*7 = 2520.\r
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\n" ); document.write( "\n" ); document.write( "Now it is clear that the required number  N  less than  3000  does exist and is unique.\r
\n" ); document.write( "\n" ); document.write( "It is the number  2521.\r
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\n" ); document.write( "\n" ); document.write( "Thank you for submitting this problem.\r
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