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Wikipedia:Reference desk/Archives/Mathematics/2017 March 10

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March 10

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Odd number divisible by its half + 0.5

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Is there any odd number n that can be divided by n/2 + 0.5? Is there any proof in wiki that this is impossible? Hofhof (talk) 20:25, 10 March 2017 (UTC)[reply]

@Hofhof: The only such odd number is 1. Let for an integer k; then , and -1 is not zero modulo (k + 1) unless n is 1.--Jasper Deng (talk) 20:40, 10 March 2017 (UTC)[reply]
If you allow negative numbers, -3 also works.--Jasper Deng (talk) 20:44, 10 March 2017 (UTC)[reply]
Or much simpler:
if and only if . Ruslik_Zero 20:50, 10 March 2017 (UTC)[reply]
Are odd?Hofhof (talk) 21:36, 10 March 2017 (UTC)[reply]