n is an integer.
(n-2) is divisible by 3 and 5,
(n-3) is divisible by 8,
What is the smallest possible value of n??
My solution is the following:
(n-2)=15k, where k is an integer, since it is divisible by 3 and 5
So (n-3)=15k-1 is divisible by 8, k=1, 2, 3, ...
The smallest number k such that (n-3) is divisible by 8 is k=7 (*)
Is there any other ways to solve this without listing all the possible values of (n-3) in step (*) and determine
whether (n-3) is divisible by 8.
Because if the smallest k is very big, then I will have a long list of numbers b4 I can get the answer.
Anyone can help?