^{2}ends with 0 if and only if n ends with 0. Now consider integers represented in base b, where 5 <= b <= 9. Determine for which base b (if any) the following statement is true:

^{2}ends with 0 if and only if n ends with 0.

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Guest Message by DevFuse

Started by BMAD, May 27 2013 07:05 PM

6 replies to this topic

Posted 27 May 2013 - 07:05 PM

Suppose n is an integer in base 10. Note that n^{2} ends with 0 if and only if n ends with 0. Now consider integers represented in base b, where 5 <= b <= 9. Determine for which base b (if any) the following statement is true:

For any integer n, n^{2} ends with 0 if and only if n ends with 0.

Posted 27 May 2013 - 07:45 PM

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Posted 27 May 2013 - 08:38 PM

i'm pretty sure that statement is true for any base.

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Posted 28 May 2013 - 02:45 AM

i'm pretty sure that statement is true for any base.

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Posted 28 May 2013 - 08:58 AM

okay i see. i was reading "only if" more literally rather than its actual inverse statement.

Posted 28 May 2013 - 12:22 PM

Spoiler for

Posted 28 May 2013 - 07:27 PM

Spoiler for As a general rule

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