Challenge: find the first value where two functions differ

[Ian Kelly]

On Fri, Aug 4, 2017 at 9:47 AM, Chris Angelico <rosuav at gmail.com> wrote:
> On Sat, Aug 5, 2017 at 1:44 AM, Chris Angelico <rosuav at gmail.com> wrote:
>> That gave me this result almost instantaneously:
>>
>> 4503599761588224
>>
>> which has been rounded up instead of down. I don't know if that counts
>> as sufficiently wrong?
>
> Oh, and I forgot to say: I have no actual *proof* that this is the
> lowest number for which this will occur. It does not occur with
> 4503599761588223 (the next lower integer), but could happen with
> something between two squares, for all I know. However, I suspect that
> it wouldn't.

Your example demonstrates that the "2**53 < M" assumption was wrong,
which is interesting. It may be worth checking values less than 2**26
as well.