The discussion revolves around proving a statement by induction related to nonnegative integers and their representation in terms of a fixed positive integer. The original poster seeks assistance in understanding the application of induction in this context.
There is an ongoing exploration of the problem, with participants providing insights into the base case of the induction and discussing the implications of adding 1 to the equation. No consensus has been reached, but there are indications of productive lines of reasoning being developed.
Participants note the importance of the fixed positive integer b and the implications this has on the proof. The original poster's request for clarification on induction suggests a potential gap in understanding the method itself.
voko said:Are there any restrictions on q and b? Otherwise the statement is trivially satisfied by q = n, b = 1, r = 0.
voko said:Are there any restrictions on q and b? Otherwise the statement is trivially satisfied by q = n, b = 1, r = 0.
You can easily check that it's true for [itex]n = 0[/itex]. Now suppose it's true for [itex]n[/itex], so there exist [itex]q[/itex] and [itex]r < b[/itex] such that [itex]n = qb + r[/itex]. Now consider [itex]n + 1[/itex]. A reasonable first step would be to add 1 to both sides of the equation above:zjhok2004 said:Can someone help me on how to solve this question? and how does induction works here?
thank you