A={the set of all positive integers leaving a remainder of 4 when divided by 45}
B={the set of all positive integers leaving a remainder of 45 when divided by 454}
C={the set of all positive integers leaving a remainder of 454 when divided by 4545}
D={the set of all positive integers leaving a remainder of 4545 when divided by 45454}

Find the smallest number in the intersection of
1)Sets A and B;
2)Sets A and B and C;
3)Sets A and B and C and D.

I get 499 for part 1. (Euclid's algorithm gives  45*111 - 454*11 = 1 and then 45*11 - 454*1 = 41.)

Edited on April 15, 2006, 3:38 pm

Posted by Richard on 2006-04-15 15:27:53