I was playing around with a few numbers.I noticed the following:
Given two coprime naturals $a$ and $b$,we can express a lot of integers in the form $xa+yb=d$ for $x,y\ge0$ and $x$ and $y$ are integers.
However, there are some others which I could not express in the form I just described.For example, if $a=7$ and $b=5$, I could not express 1,2,3,4,6,8,9,11,13,16,18 and 23 as above.There might be more of them.That brought to my mind a question.
Given two coprime positive integers $(a,b),a>1,b>1$,is the number of natural numbers which cannot be expressed in the form above finite? Can we exactly calculate how many of them exist?.