What is the smallest number which leaves a remainder:
9 when divided by 10;
8 when divided by 9;
7 when divided by 8;
6 when divided by 7;
5 when divided by 6;
4 when divided by 5;
3 when divided by 4;
2 when divided by 3;
1 when divided by 2 ?

[ In other words: Find the Least number which when divided by 'N' leaves a remainder '(N-1)', for N = 1,2,3,4,........,9,10].

the number is (2^3)*(3^2)*5*7 - 1
logic for any number 'p':
obtain all prime factors occuring in numbers upto 'p' (in their maximum powers of occurence). the number thus obtained shall be of the form 1k and 2k and 3k.... till pk where k is any natural no. if you subtract one from it you shall get the required form.

Posted by spinoza on 2003-06-01 02:36:12