1 and 20 are first and last terms of the arithmetic progression. If all the terms of this arithmetic progression are integers, then find the different number of terms that this arithmetic progression can have ?
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Here's an obvious generalization which may be interesting to you, and which exposes the reasoning for the question above: $1$ and $(1+p)$ are the first and last terms of an arithmetic progression, where $p$ is prime. If all the terms of this arithmetic progression are integers, how many different number of terms can this arithmetic progression have?
See if you can generalize Henning's comment regarding your original question which was that the number of terms $k$ with step size $s$ must satisfy $1+s(k-1)=20$ in order to answer this question as well.