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Reference.org
Kummer's theorem
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, Kummer's theorem is a formula for the exponent of the highest power of a <a href="/facts/Prime_number/L20FLkgn">prime number</a> <i>p</i> that divides a given binomial coefficient. In other words, it gives the <a href="/facts/P-adic_valuation/wktvC3UP"><i>p</i>-adic valuation</a> of a <a href="/facts/Binomial_coefficient/Tsx7eY5h">binomial coefficient</a>. The theorem is named after <a href="/facts/Ernst_Kummer/dGnaTQyG">Ernst Kummer</a>, who proved it in 1852 (Kummer 1852). </p>