Re: May we trust IntegerQ ?

• To: mathgroup at smc.vnet.net
• Subject: [mg107511] Re: [mg107488] May we trust IntegerQ ?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 15 Feb 2010 05:47:43 -0500 (EST)

```Actually, I do not really understand the point of the question. IntegerQ
is obviously not the way to test if something is an integer, it will
only return True for expressions which are explicit integers. So

IntegerQ[ChebyshevT[7/2, 7]]

False

The right way to deal with this kind of problem is:

Element[ChebyshevT[7/2, 7], Integers] // FullSimplify

True

Andrzej Kozlowski

On 14 Feb 2010, at 15:14, Andrzej Kozlowski wrote:

>
> On 14 Feb 2010, at 14:16, Artur wrote:
>
>> Procedure: find such x that ChebyshevT[x/2, x] isn't integer
>> aa = {}; Do[ If[IntegerQ[ChebyshevT[x/2, x]], , AppendTo[aa, x]],
{x, 0,
>> 20}]; aa
>> and answer Mathematica is set:
>> {3, 5, 7, 9, 11, 13, 15, 17, 19}
>> where occered e.g. number 7
>> N[ChebyshevT[7/2, 7],100]
>> =
5042.00000000000000000000000000000000000000000000000000000000000000000\
>> 0000000000000000000000000000000
>> evidently is integer 5042
>>
>> Best wishes
>> Artur
>>
>>
>>
>>
>
> FunctionExpand[ChebyshevT[7/2, 7]]
>
> 5042
>
> so it definitely is an integer.
>
> Andrzej Kozlowski

```

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