The numbers 637, 638, and 639 constitute a set of three consecutive positive integers (in order) that are respectively divisible by 13, 11, and 9.
Find the first set of four consecutive positive integers (in order) that are respectively divisible by 13, 11, 9, and 7.
How about the first set of five consecutive positive integers (in order) that are respectively divisible by 13, 11, 9, 7, and 5?
Four consecutive integers are 13A, 11B, 9C, 7D.
13A + 3 = 7D
A = 3 mod 7
A = 3 + 7E
13A = 39 +91E
39 +91E + 2 = 9C
E = 4 mod 9
E = 4 + 9F
13A = 403 + 819F
403 + 819F + 1 = 11B
F = 5 mod 11
F = 5 + 11G
13A = 4498 + 9009G
Set G = 0 to get 4498, 4499, 4500, 4501.
Part 2 can be approached in a similar manner.
|
|
Posted by xdog
on 2023-02-10 09:21:45 |
Solution Part 1
