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Undergraduate
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Primes and divisibility
Prove the following without using Fermat's little theorem or Euler's totient theorem. Here \(a\ |\ b\) means \(a\) divides \(b\). Prove that for every prime number \(p\) and every pair of integer…
Mathematics
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divisibility
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True IMO
on Oct. 9, 2012 | Updated Jan. 4, 2018
International Mathematical Olympiad 1998 Problem 3
For any positive integer \(n\), let \(d(n)\) denote the number of positive divisors of \(n\) (including \(1\) and \(n\) itself). Determine all positive integers \(k\) such that \(d(n^2)/d(n) = k\) for…
Mathematics
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divisibility
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imo 1998
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Undergraduate
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rajeshchitnis
on Aug. 2, 2012 | Updated Dec. 6, 2017
Numbers divisible by sum of their digits
Show that there is an infinite sequence of natural numbers \({p_1,p_2,\ldots}\) such that for every \(i\in \mathbb{N}\) the number \(p_i\) does not have 0 as any of its digits but is divisible by the …
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