Inspired by Ivan Koswara
Does there exist a non-constant arithmetic progression (AP) of 10 positive integers that does not contain the digit 9?
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2 solutions
@Calvin Lin May be you should mention that the AP is of integers.Otherwise, the answer becomes trivial ;p
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Hm, How does it become trivialized?
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Consider any AP of non-integer rational terms.You won't find "digit" 9 in it XD
Because it's meaningless to talk about whether a digit exists in a non-integer.
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It contains the digit 9 (in 97).
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Thanks I edited it now is it correct?
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@Abc Xyz – Yes, it is now correct. Essentially the same thing as the solution above.
Exactly the same example I had in my mind
If it does not require positive terms, we always have:
− 5 , − 4 , − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , 4
The question was edited to only have positive integers, and here's another example:
5 , 1 0 , 1 5 , 2 0 , 2 5 , 3 0 , 3 5 , 4 0 , 4 5 , 5 0
Therefore, Yes, there exists such an AP
Ah, good point! Let me add in the requirement for positive terms.
In your second series it contains the digit 9 (the terms 90 and 95)
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We only need a progression of 1 0 terms
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Oh OK ! Sorry....Because Ivan had told me so when I had uploaded something similar
The most simple example of such an AP is : 2 , 4 , 6 , 8 , 1 0 , 1 2 , 1 4 , 1 6 , 1 8 , 2 0